Mathematische Zeitschrift, ISSN 0025-5874, 6/2012, Volume 271, Issue 1, pp. 447 - 467

We point out some of the differences between the consequences of p-Poincaré inequality and that of...

Primary 46E35 | Secondary 30L10 | {{\mathcal{A}}_{\infty}}$$ weights | Poincaré inequalities | Mathematics, general | 31E05 | Mathematics | Thick quasiconvexity | Metric measure spaces | weights

Primary 46E35 | Secondary 30L10 | {{\mathcal{A}}_{\infty}}$$ weights | Poincaré inequalities | Mathematics, general | 31E05 | Mathematics | Thick quasiconvexity | Metric measure spaces | weights

Journal Article

2005, 1st ed., North-Holland mathematical library, ISBN 9780444517951, Volume 67, 606

The book addresses many important new developments in the field. All the topics covered are of great interest to the readers because such inequalities have become a major tool in the analysis of various branches of mathematics...

Inequalities (Mathematics)

Inequalities (Mathematics)

eBook

Proceedings of the American Mathematical Society, ISSN 0002-9939, 09/2015, Volume 143, Issue 9, pp. 4017 - 4028

In various analytical contexts, it is proved that a weak Sobolev inequality implies a doubling property for the underlying measure.

Subunit metric spaces | Sobolev inequality | Moser iteration | Doubling condition | subunit metric spaces | LOCAL DIRICHLET SPACES | MATHEMATICS, APPLIED | doubling condition | MINIMIZERS | FORMS | LAPLACIAN | MATHEMATICS | PARABOLIC HARNACK INEQUALITIES | REGULARITY | POINCARE INEQUALITIES | HEAT KERNEL

Subunit metric spaces | Sobolev inequality | Moser iteration | Doubling condition | subunit metric spaces | LOCAL DIRICHLET SPACES | MATHEMATICS, APPLIED | doubling condition | MINIMIZERS | FORMS | LAPLACIAN | MATHEMATICS | PARABOLIC HARNACK INEQUALITIES | REGULARITY | POINCARE INEQUALITIES | HEAT KERNEL

Journal Article

Journal of functional analysis, ISSN 0022-1236, 2010, Volume 259, Issue 8, pp. 2045 - 2072

We prove a new inequality which improves on the classical Hardy inequality in the sense that a nonlinear integral quantity with super-quadratic growth, which is computed with respect to an inverse...

Caffarelli–Kohn–Nirenberg inequalities | Interpolation | Scale invariance | Hardy–Sobolev inequalities | Emden–Fowler transformation | Hardy inequality | Radial symmetry | Sobolev inequality | Logarithmic Sobolev inequality | Symmetry breaking | Caffarelli-Kohn-Nirenberg inequalities | Hardy-Sobolev inequalities | Emden-Fowler transformation | CONVEX SOBOLEV INEQUALITIES | SPHERE | MATHEMATICS | SYMMETRY | POINCARE | KOHN-NIRENBERG INEQUALITIES | EXTREMAL-FUNCTIONS | SHARP CONSTANTS | EQUATION | Equality | Analysis of PDEs | Mathematics

Caffarelli–Kohn–Nirenberg inequalities | Interpolation | Scale invariance | Hardy–Sobolev inequalities | Emden–Fowler transformation | Hardy inequality | Radial symmetry | Sobolev inequality | Logarithmic Sobolev inequality | Symmetry breaking | Caffarelli-Kohn-Nirenberg inequalities | Hardy-Sobolev inequalities | Emden-Fowler transformation | CONVEX SOBOLEV INEQUALITIES | SPHERE | MATHEMATICS | SYMMETRY | POINCARE | KOHN-NIRENBERG INEQUALITIES | EXTREMAL-FUNCTIONS | SHARP CONSTANTS | EQUATION | Equality | Analysis of PDEs | Mathematics

Journal Article

Potential Analysis, ISSN 0926-2601, 2/2012, Volume 36, Issue 2, pp. 317 - 337

We study the connection between the p-Talagrand inequality and the q-logarithmic Sololev inequality for conjugate exponents p ≥ 2, q...

Geodesic metric space | Hamilton–Jacobi semigroup | Probability Theory and Stochastic Processes | Mathematics | Secondary 36C05 | Geometry | Primary 70H20 | 49L99 | 47D06 | Potential Theory | Functional Analysis | Poincaré inequalities | Logarithmic–Sobolev inequalites | Talagrand inequalites | Metric-measure space | Hamilton-Jacobi semigroup | Logarithmic-Sobolev inequalites | METRIC-MEASURE-SPACES | TRANSPORTATION COST | HOPF-LAX FORMULA | BRASCAMP | MATHEMATICS | MAPS | Poincare inequalities | GEOMETRY

Geodesic metric space | Hamilton–Jacobi semigroup | Probability Theory and Stochastic Processes | Mathematics | Secondary 36C05 | Geometry | Primary 70H20 | 49L99 | 47D06 | Potential Theory | Functional Analysis | Poincaré inequalities | Logarithmic–Sobolev inequalites | Talagrand inequalites | Metric-measure space | Hamilton-Jacobi semigroup | Logarithmic-Sobolev inequalites | METRIC-MEASURE-SPACES | TRANSPORTATION COST | HOPF-LAX FORMULA | BRASCAMP | MATHEMATICS | MAPS | Poincare inequalities | GEOMETRY

Journal Article

The Journal of geometric analysis, ISSN 1050-6926, 12/2018, Volume 28, Issue 4, pp. 3522 - 3552

Extremal functions are exhibited in Poincare trace inequalities for functions of bounded variation in the unit ball Bn of the n-dimensional Euclidean spaceRn...

Isoperimetric inequalities | Functions of bounded variation | Sobolev spaces | Boundary traces | Poincaré inequalities | Sharp constants | ISOPERIMETRIC INEQUALITY | CONSTANT | SOBOLEV INEQUALITIES | MATHEMATICS | BALLS | WORST | EXTREMAL-FUNCTIONS | Poincare inequalities

Isoperimetric inequalities | Functions of bounded variation | Sobolev spaces | Boundary traces | Poincaré inequalities | Sharp constants | ISOPERIMETRIC INEQUALITY | CONSTANT | SOBOLEV INEQUALITIES | MATHEMATICS | BALLS | WORST | EXTREMAL-FUNCTIONS | Poincare inequalities

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 8/2016, Volume 165, Issue 3, pp. 667 - 723

We prove a new class of inequalities, yielding bounds for the normal approximation in the Wasserstein and the Kolmogorov distance of functionals of a general Poisson process...

60D05 | Stein’s method | Stabilization | Theoretical, Mathematical and Computational Physics | 60G60 | Probability Theory and Stochastic Processes | Mathematics | Poisson process | Spatial Ornstein-Uhlenbeck process | Poincaré inequality | Stochastic geometry | Chaos expansion | Nearest neighbour graph | 60H07 | Operation Research/Decision Theory | 60F05 | 60G55 | Mathematical and Computational Biology | Voronoi tessellation | Quantitative Finance | Kolmogorov distance | Central limit theorem | Statistics for Business/Economics/Mathematical Finance/Insurance | Mehler’s formula | Wasserstein distance | Malliavin calculus | Studies | Poisson distribution | Mathematical analysis | Approximations | Operators | Approximation | Functionals | Inequalities | Nonlinearity | Estimates

60D05 | Stein’s method | Stabilization | Theoretical, Mathematical and Computational Physics | 60G60 | Probability Theory and Stochastic Processes | Mathematics | Poisson process | Spatial Ornstein-Uhlenbeck process | Poincaré inequality | Stochastic geometry | Chaos expansion | Nearest neighbour graph | 60H07 | Operation Research/Decision Theory | 60F05 | 60G55 | Mathematical and Computational Biology | Voronoi tessellation | Quantitative Finance | Kolmogorov distance | Central limit theorem | Statistics for Business/Economics/Mathematical Finance/Insurance | Mehler’s formula | Wasserstein distance | Malliavin calculus | Studies | Poisson distribution | Mathematical analysis | Approximations | Operators | Approximation | Functionals | Inequalities | Nonlinearity | Estimates

Journal Article

SIAM journal on numerical analysis, ISSN 0036-1429, 1/2014, Volume 52, Issue 6, pp. 2957 - 2976

.... The key to the estimates is an improved "streamline" Poincaré–Friedrichs inequality.

Error rates | Boundary value problems | Algebra | Inner products | Vector fields | Boundary conditions | Research grants | Iterative methods | Mathematical preconditioning | Convection | Streamline diffusion finite element method | Robust preconditioning | Poincaré-Friedrichs inequality | Poincare-Friedrichs inequality | MATHEMATICS, APPLIED | NONSYMMETRIC SYSTEMS | DIFFUSION PROBLEMS | LINEAR-EQUATIONS | streamline diffusion finite element method | ITERATIVE METHODS | CONJUGATE-GRADIENT | robust preconditioning | Equivalence | Perturbation methods | Inequalities | Fields (mathematics) | Diffusion | Estimates | Preconditioning | Convergence

Error rates | Boundary value problems | Algebra | Inner products | Vector fields | Boundary conditions | Research grants | Iterative methods | Mathematical preconditioning | Convection | Streamline diffusion finite element method | Robust preconditioning | Poincaré-Friedrichs inequality | Poincare-Friedrichs inequality | MATHEMATICS, APPLIED | NONSYMMETRIC SYSTEMS | DIFFUSION PROBLEMS | LINEAR-EQUATIONS | streamline diffusion finite element method | ITERATIVE METHODS | CONJUGATE-GRADIENT | robust preconditioning | Equivalence | Perturbation methods | Inequalities | Fields (mathematics) | Diffusion | Estimates | Preconditioning | Convergence

Journal Article

Revista matemática iberoamericana, ISSN 0213-2230, 2018, Volume 34, Issue 3, pp. 1021 - 1054

.... In particular these formulae entail new functional inequalities of Brascamp-Lieb type for log-concave distributions and beyond...

Log-concave probability measure | Brascamp-Lieb type inequalities | Diffusion operator on vector fields | Spectral gap | Intertwining | LOGARITHMIC SOBOLEV INEQUALITIES | DECAY | BRUNN-MINKOWSKI | CONCAVE PROBABILITY-MEASURES | COMPLETE RIEMANNIAN MANIFOLD | log- concave probability measure | ONE-DIMENSIONAL DIFFUSIONS | MATHEMATICS | POINCARE | spectral gap | SPIN SYSTEMS | EQUATION | diffusion operator on vector fields

Log-concave probability measure | Brascamp-Lieb type inequalities | Diffusion operator on vector fields | Spectral gap | Intertwining | LOGARITHMIC SOBOLEV INEQUALITIES | DECAY | BRUNN-MINKOWSKI | CONCAVE PROBABILITY-MEASURES | COMPLETE RIEMANNIAN MANIFOLD | log- concave probability measure | ONE-DIMENSIONAL DIFFUSIONS | MATHEMATICS | POINCARE | spectral gap | SPIN SYSTEMS | EQUATION | diffusion operator on vector fields

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 2019, Volume 294, Issue 1-2, pp. 17 - 49

.... In this paper, we consider an n-Ahlfors regular rectifiable set M subset of Rn+d that satisfies a Poincare-type inequality involving Lipschitz functions and their tangential derivatives...

Rectifiable set | Bi-Lipschitz image | Ahlfors regular | Carleson-type condition | p-Poincaré inequality | Poincaré-type condition | MATHEMATICS | p-Poincare inequality | Poincare-type condition | SPACES | RICCI CURVATURE | CHORD ARC SURFACES

Rectifiable set | Bi-Lipschitz image | Ahlfors regular | Carleson-type condition | p-Poincaré inequality | Poincaré-type condition | MATHEMATICS | p-Poincare inequality | Poincare-type condition | SPACES | RICCI CURVATURE | CHORD ARC SURFACES

Journal Article

Journal of theoretical probability, ISSN 1572-9230, 2019, Volume 33, Issue 1, pp. 396 - 427

We present an improved version of the second-order Gaussian Poincare inequality, first introduced in Chatterjee...

Isonormal Gaussian processes | Functionals of Gaussian fields | Wigner matrices | Central limit theorems | Gaussian approximation | Second-order Poincaré inequalities | CENTRAL LIMIT-THEOREMS | WIENER | SEQUENCES | CONVERGENCE | STATISTICS & PROBABILITY | Second-order Poincare inequalities

Isonormal Gaussian processes | Functionals of Gaussian fields | Wigner matrices | Central limit theorems | Gaussian approximation | Second-order Poincaré inequalities | CENTRAL LIMIT-THEOREMS | WIENER | SEQUENCES | CONVERGENCE | STATISTICS & PROBABILITY | Second-order Poincare inequalities

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2019, Volume 266, Issue 1, pp. 44 - 69

Let X be a noncomplete metric measure space satisfying the usual (local) assumptions of a doubling property and a Poincaré inequality...

Newtonian Sobolev space | Lebesgue point | Quasiminimizer | Noncomplete metric space | p-harmonic function | Poincaré inequality | QUASICONTINUITY | QUASIMINIMIZERS | LIPSCHITZ FUNCTIONS | POTENTIAL-THEORY | OPEN SETS | MATHEMATICS | QUASIOPEN | Poincare inequality | HARMONIC-FUNCTIONS

Newtonian Sobolev space | Lebesgue point | Quasiminimizer | Noncomplete metric space | p-harmonic function | Poincaré inequality | QUASICONTINUITY | QUASIMINIMIZERS | LIPSCHITZ FUNCTIONS | POTENTIAL-THEORY | OPEN SETS | MATHEMATICS | QUASIOPEN | Poincare inequality | HARMONIC-FUNCTIONS

Journal Article

Publications of the Research Institute for Mathematical Sciences, ISSN 0034-5318, 2017, Volume 53, Issue 1, pp. 119 - 139

We establish two-weight norm inequalities for singular integral operators and fractional integral operators on Morrey spaces...

Singular integral operator | Stein–Weiss inequality | Rellich inequality | Two-weight norm inequality | Hardy inequality | Fractional integral operator | Sobolev inequality | Morrey space | Poincaré inequality | SINGULAR INTEGRAL-OPERATORS | fractional integral operator | UNIQUE CONTINUATION | FRACTIONAL INTEGRALS | MATHEMATICS | Stein-Weiss inequality | WEIGHTED INEQUALITIES | MAXIMAL OPERATORS | singular integral operator | Poincare inequality | DEGENERATE ELLIPTIC-EQUATIONS | VARIABLE EXPONENTS | SHARP 2-WEIGHT

Singular integral operator | Stein–Weiss inequality | Rellich inequality | Two-weight norm inequality | Hardy inequality | Fractional integral operator | Sobolev inequality | Morrey space | Poincaré inequality | SINGULAR INTEGRAL-OPERATORS | fractional integral operator | UNIQUE CONTINUATION | FRACTIONAL INTEGRALS | MATHEMATICS | Stein-Weiss inequality | WEIGHTED INEQUALITIES | MAXIMAL OPERATORS | singular integral operator | Poincare inequality | DEGENERATE ELLIPTIC-EQUATIONS | VARIABLE EXPONENTS | SHARP 2-WEIGHT

Journal Article

Revista matemática iberoamericana, ISSN 0213-2230, 2014, Volume 30, Issue 1, pp. 109 - 131

By adapting some ideas of M. Ledoux ([12], [13] and [14]) to a sub-Riemannian framework we study Sobolev, Poincare and isoperimetric inequalities associated...

Isoperimetric inequality | Subelliptic operator | Sobolev inequalities | Poincaré inequality | MATHEMATICS | isoperimetric inequality | Poincare inequality | subelliptic operator | 1ST EIGENVALUE

Isoperimetric inequality | Subelliptic operator | Sobolev inequalities | Poincaré inequality | MATHEMATICS | isoperimetric inequality | Poincare inequality | subelliptic operator | 1ST EIGENVALUE

Journal Article

Mathematical and computer modelling, ISSN 0895-7177, 2010, Volume 52, Issue 3-4, pp. 556 - 566

Here we develop the Delta Fractional Calculus on Time Scales. Then we produce related integral inequalities of types: Poincaré...

Delta Sobolev inequality | Fractional calculus on time scales | Delta Hilbert–Pachpatte inequality | Delta Ostrowski inequality | Delta Opial inequality | Delta Poincaré inequality | Delta Hilbert-Pachpatte inequality | MATHEMATICS, APPLIED | Delta Poincare inequality

Delta Sobolev inequality | Fractional calculus on time scales | Delta Hilbert–Pachpatte inequality | Delta Ostrowski inequality | Delta Opial inequality | Delta Poincaré inequality | Delta Hilbert-Pachpatte inequality | MATHEMATICS, APPLIED | Delta Poincare inequality

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 12/2016, Volume 18, Issue 6, p. 1550086

In this paper, we prove a sharp upper bound for the first nontrivial eigenvalue of the
p
-Laplacian with Neumann boundary conditions. This applies to convex...

shape optimization | Nonlinear eigenvalue problems | EIGENVALUE | MATHEMATICS | MATHEMATICS, APPLIED | CONSTANTS | LOWER BOUNDS | POINCARE INEQUALITIES

shape optimization | Nonlinear eigenvalue problems | EIGENVALUE | MATHEMATICS | MATHEMATICS, APPLIED | CONSTANTS | LOWER BOUNDS | POINCARE INEQUALITIES

Journal Article

Positivity, ISSN 1385-1292, 7/2018, Volume 22, Issue 3, pp. 687 - 699

In this paper we prove the Poincaré-type weighted inequality $$\begin{aligned} \Vert v^{1/q} f \Vert _{L^q(\Omega )} \le C \Vert \omega ^{1/p} \nabla f \Vert...

Convex domain | 26D10 | Change of variables | 35J70 | 35A23 | Mathematics | 35J15 | Poincaré inequality | Operator Theory | Fourier Analysis | Potential Theory | Weights | Fubini’s theorem | Calculus of Variations and Optimal Control; Optimization | Econometrics | Equality | Inequality

Convex domain | 26D10 | Change of variables | 35J70 | 35A23 | Mathematics | 35J15 | Poincaré inequality | Operator Theory | Fourier Analysis | Potential Theory | Weights | Fubini’s theorem | Calculus of Variations and Optimal Control; Optimization | Econometrics | Equality | Inequality

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 477, Issue 2, pp. 1157 - 1181

In this paper, we establish several Poincaré–Sobolev type inequalities concerning to the Laplace–Beltrami operator Δ...

Hyperbolic spaces | Decreasing spherical symmetric rearrangement | Sobolev inequality | Adams inequality with exact growth | Poincaré–Sobolev inequality | Adams inequality

Hyperbolic spaces | Decreasing spherical symmetric rearrangement | Sobolev inequality | Adams inequality with exact growth | Poincaré–Sobolev inequality | Adams inequality

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 4/2019, Volume 29, Issue 2, pp. 1608 - 1648

This work explores new deep connections between John–Nirenberg type inequalities and Muckenhoupt weight invariance for a large class of BMO-type spaces...

Abstract Harmonic Analysis | Fourier Analysis | Weight invariance | John–Nirenberg inequality | BMO | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Mathematics | Differential Geometry | Dynamical Systems and Ergodic Theory | Spaces of bounded mean oscillations | Muckenhoupt weights | SELF-IMPROVING PROPERTIES | APPROXIMATIONS | IDENTITY | MATHEMATICS | REVERSE HOLDER PROPERTY | IMPROVEMENT | DUALITY | John-Nirenberg inequality | BOUNDED MEAN-OSCILLATION | POINCARE INEQUALITIES | HARDY

Abstract Harmonic Analysis | Fourier Analysis | Weight invariance | John–Nirenberg inequality | BMO | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Mathematics | Differential Geometry | Dynamical Systems and Ergodic Theory | Spaces of bounded mean oscillations | Muckenhoupt weights | SELF-IMPROVING PROPERTIES | APPROXIMATIONS | IDENTITY | MATHEMATICS | REVERSE HOLDER PROPERTY | IMPROVEMENT | DUALITY | John-Nirenberg inequality | BOUNDED MEAN-OSCILLATION | POINCARE INEQUALITIES | HARDY

Journal Article

Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, ISSN 0308-2105, 2019, Volume 150, Issue 4, pp. 1699 - 1736

We prove optimal improvements of the Hardy inequality on the hyperbolic space. Here, optimal means that the resulting operator iscriticalin the sense of Devyver, Fraas, and Pinchover (2014...

optimal Hardy inequality | extremals | Hyperbolic space | MATHEMATICS | MATHEMATICS, APPLIED | RELLICH INEQUALITIES | EQUATIONS | POINCARE INEQUALITIES | RIEMANNIAN-MANIFOLDS | Manifolds | Inequalities | Inequality

optimal Hardy inequality | extremals | Hyperbolic space | MATHEMATICS | MATHEMATICS, APPLIED | RELLICH INEQUALITIES | EQUATIONS | POINCARE INEQUALITIES | RIEMANNIAN-MANIFOLDS | Manifolds | Inequalities | Inequality

Journal Article

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