Advances in Mathematics, ISSN 0001-8708, 2009, Volume 220, Issue 4, pp. 1222 - 1264

A multi(sub)linear maximal operator that acts on the product of m Lebesgue spaces and is smaller than the m-fold product of the Hardy–Littlewood maximal...

Weighted norm inequalities | Commutators | Multilinear singular integrals | Calderón–Zygmund theory | Maximal operators | Calderón-Zygmund theory | NORM INEQUALITIES | SPACES | Calderon-Zygmund theory | EQUATIONS | SINGULAR INTEGRAL-OPERATORS | MEAN OSCILLATION | CONJECTURE | EXTRAPOLATION | MATHEMATICS | COEFFICIENTS | VARIABLES

Weighted norm inequalities | Commutators | Multilinear singular integrals | Calderón–Zygmund theory | Maximal operators | Calderón-Zygmund theory | NORM INEQUALITIES | SPACES | Calderon-Zygmund theory | EQUATIONS | SINGULAR INTEGRAL-OPERATORS | MEAN OSCILLATION | CONJECTURE | EXTRAPOLATION | MATHEMATICS | COEFFICIENTS | VARIABLES

Journal Article

Advances in Mathematics, ISSN 0001-8708, 01/2002, Volume 165, Issue 1, pp. 124 - 164

A systematic treatment of multilinear Calderón–Zygmund operators is presented. The theory developed includes strong type and endpoint weak type estimates,...

multilinear operators | interpolation | Calderón–Zygmund singular integrals | multipliers | pseudodifferential operators | T1 Theorem | Calderó | Zygmund singular integrals | Interpolation | Multilinear operators | Multipliers | Pseudodifferential operators | Calderón-Zygmund singular integrals | T1 theorem | MATHEMATICS | multipliers interpolation | Calderon Zygmund singular integrals | OPERATORS

multilinear operators | interpolation | Calderón–Zygmund singular integrals | multipliers | pseudodifferential operators | T1 Theorem | Calderó | Zygmund singular integrals | Interpolation | Multilinear operators | Multipliers | Pseudodifferential operators | Calderón-Zygmund singular integrals | T1 theorem | MATHEMATICS | multipliers interpolation | Calderon Zygmund singular integrals | OPERATORS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 07/2019, Volume 372, Issue 7, pp. 4761 - 4803

We introduce a class of operators on abstract measure spaces that unifies the Calderón-Zygmund operators on spaces of homogeneous type, the maximal functions,...

SPACES | martingale transform | WEIGHTED NORM INEQUALITIES | PROOF | POINTWISE ESTIMATE | weighted inequalities | MATHEMATICS | Calderon-Zygmund operator | maximal function | BOUNDS | sparse operators | homogeneous spaces | CALDERON-ZYGMUND OPERATORS

SPACES | martingale transform | WEIGHTED NORM INEQUALITIES | PROOF | POINTWISE ESTIMATE | weighted inequalities | MATHEMATICS | Calderon-Zygmund operator | maximal function | BOUNDS | sparse operators | homogeneous spaces | CALDERON-ZYGMUND OPERATORS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 11/2012, Volume 263, Issue 10, pp. 3117 - 3143

We consider a nonhomogeneous elliptic problem with an irregular obstacle involving a discontinuous nonlinearity over an irregular domain in divergence form of...

Discontinuous nonlinearity | p-Laplacian | Irregular obstacle | Calderón–Zygmund estimate | BMO | Reifenberg domain | P-Laplacian | Calderón-Zygmund estimate | INTEGRABILITY | PARABOLIC EQUATIONS | Calderon-Zygmund estimate | MATHEMATICS | REGULARITY | PARTIAL-DIFFERENTIAL EQUATIONS | REIFENBERG DOMAINS | GROWTH | COEFFICIENTS

Discontinuous nonlinearity | p-Laplacian | Irregular obstacle | Calderón–Zygmund estimate | BMO | Reifenberg domain | P-Laplacian | Calderón-Zygmund estimate | INTEGRABILITY | PARABOLIC EQUATIONS | Calderon-Zygmund estimate | MATHEMATICS | REGULARITY | PARTIAL-DIFFERENTIAL EQUATIONS | REIFENBERG DOMAINS | GROWTH | COEFFICIENTS

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 06/2020, Volume 138, pp. 356 - 412

We develop a wide general theory of bilinear bi-parameter singular integrals T. This includes general Calderón–Zygmund type principles in the bilinear...

Calderón–Zygmund operators | Bilinear analysis | Commutators | Bi-parameter analysis

Calderón–Zygmund operators | Bilinear analysis | Commutators | Bi-parameter analysis

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2013, Volume 397, Issue 2, pp. 785 - 790

We construct a family of n+1 dyadic filtrations in Rn, so that every Euclidean ball B is contained in some cube Q of our family satisfying diam(Q)≤cndiam(B)...

Calderón–Zygmund operators | Dyadic harmonic analysis | Covering lemmas | Calderón-Zygmund operators | MATHEMATICS | NONHOMOGENEOUS SPACES | MATHEMATICS, APPLIED | BMO | Calderon-Zygmund operators | OPERATORS | SINGULAR-INTEGRALS

Calderón–Zygmund operators | Dyadic harmonic analysis | Covering lemmas | Calderón-Zygmund operators | MATHEMATICS | NONHOMOGENEOUS SPACES | MATHEMATICS, APPLIED | BMO | Calderon-Zygmund operators | OPERATORS | SINGULAR-INTEGRALS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 11/2013, Volume 248, pp. 736 - 783

The purpose of this paper is to study the boundedness of operators of the formf{mapping}ψ(x)∫f(γt(x))K(t)dt, where (x) is a function defined on a neighborhood...

Littlewood-Paley theory | Secondary | Carnot-Carathéodory geometry | Maximal Radon transforms | Primary | Singular integrals | Flag kernels | Calderón-Zygmund theory | Product kernels | Singular Radon transforms | INTEGRALS | MATHEMATICS | Calderon-Zygmund theory | Carnot-Caratheodory geometry | SURFACES | KERNELS

Littlewood-Paley theory | Secondary | Carnot-Carathéodory geometry | Maximal Radon transforms | Primary | Singular integrals | Flag kernels | Calderón-Zygmund theory | Product kernels | Singular Radon transforms | INTEGRALS | MATHEMATICS | Calderon-Zygmund theory | Carnot-Caratheodory geometry | SURFACES | KERNELS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2009, Volume 256, Issue 2, pp. 509 - 593

The weak type ( 1 , 1 ) boundedness of singular integrals acting on matrix-valued functions has remained open since the 1980s, mainly because the methods...

Almost orthogonality | Noncommutative martingale | Calderón–Zygmund operator | Calderón-Zygmund operator | INEQUALITIES | DYADIC BMO | MARTINGALE DIFFERENCE-SEQUENCES | MATHEMATICS | OPERATOR-VALUED KERNEL | Calderon-Zygmund operator | ALGEBRAS | BANACH-SPACES | L-P-SPACES | MEASURABLE OPERATORS | HOMOGENEOUS TYPE

Almost orthogonality | Noncommutative martingale | Calderón–Zygmund operator | Calderón-Zygmund operator | INEQUALITIES | DYADIC BMO | MARTINGALE DIFFERENCE-SEQUENCES | MATHEMATICS | OPERATOR-VALUED KERNEL | Calderon-Zygmund operator | ALGEBRAS | BANACH-SPACES | L-P-SPACES | MEASURABLE OPERATORS | HOMOGENEOUS TYPE

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2007, Volume 212, Issue 1, pp. 225 - 276

This is the first part of a series of four articles. In this work, we are interested in weighted norm estimates. We put the emphasis on two results of...

Extrapolation | Singular non-integral operators | Calderón–Zygmund decomposition | Vector-valued inequalities | Commutators with bounded mean oscillation functions | Good- λ inequalities | Muckenhoupt weights | Good-λ inequalities | Calderón-Zygmund decomposition | FUNCTIONAL-CALCULUS | RIESZ TRANSFORMS | good-lambda inequalities | Calderon-Zygmund decomposition | SPACES | SQUARE ROOTS | SINGULAR INTEGRAL-OPERATORS | LIPSCHITZ-DOMAINS | commutators with bounded mean oscillation functions | singular non-integral operators | MATHEMATICS | vector-valued inequalities | extrapolation | R-N | MAXIMAL FUNCTIONS | AP WEIGHTS | NONSMOOTH KERNELS | Mathematics - Classical Analysis and ODEs

Extrapolation | Singular non-integral operators | Calderón–Zygmund decomposition | Vector-valued inequalities | Commutators with bounded mean oscillation functions | Good- λ inequalities | Muckenhoupt weights | Good-λ inequalities | Calderón-Zygmund decomposition | FUNCTIONAL-CALCULUS | RIESZ TRANSFORMS | good-lambda inequalities | Calderon-Zygmund decomposition | SPACES | SQUARE ROOTS | SINGULAR INTEGRAL-OPERATORS | LIPSCHITZ-DOMAINS | commutators with bounded mean oscillation functions | singular non-integral operators | MATHEMATICS | vector-valued inequalities | extrapolation | R-N | MAXIMAL FUNCTIONS | AP WEIGHTS | NONSMOOTH KERNELS | Mathematics - Classical Analysis and ODEs

Journal Article

Abstract and Applied Analysis, ISSN 1085-3375, 06/2008, Volume 2008, pp. 1 - 250

We work on RD-spaces 𝒳, namely, spaces of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property...

MATHEMATICS, APPLIED | SOBOLEV SPACES | LIE-GROUPS | POLYNOMIAL-GROWTH | INEQUALITIES | HARDY-SPACES | QUASI-CONFORMAL MAPPINGS | CALDERON-ZYGMUND OPERATORS | HOMOGENEOUS TYPE | FINITE-TYPE | GEOMETRY

MATHEMATICS, APPLIED | SOBOLEV SPACES | LIE-GROUPS | POLYNOMIAL-GROWTH | INEQUALITIES | HARDY-SPACES | QUASI-CONFORMAL MAPPINGS | CALDERON-ZYGMUND OPERATORS | HOMOGENEOUS TYPE | FINITE-TYPE | GEOMETRY

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2006, Volume 203, Issue 2, pp. 430 - 475

We develop a generalized Littlewood–Paley theory for semigroups acting on L p -spaces of functions with values in uniformly convex or smooth Banach spaces. We...

Uniformly convex or smooth Banach spaces | Semigroups | Vector-valued Calderón–Zygmund operators | Littlewood–Paley theory | Littlewood-Paley theory | Vector-valued Calderón-Zygmund operators | INTERPOLATION | MATHEMATICS | vector-valued Calderon-Zygmund operators | uniformly convex or smooth Banach spaces | semigroups | UNIFORMLY CONVEX-SPACES | Functional Analysis | Mathematics

Uniformly convex or smooth Banach spaces | Semigroups | Vector-valued Calderón–Zygmund operators | Littlewood–Paley theory | Littlewood-Paley theory | Vector-valued Calderón-Zygmund operators | INTERPOLATION | MATHEMATICS | vector-valued Calderon-Zygmund operators | uniformly convex or smooth Banach spaces | semigroups | UNIFORMLY CONVEX-SPACES | Functional Analysis | Mathematics

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2012, Volume 75, Issue 2, pp. 637 - 650

We prove BMO estimates of the inhomogeneous p -Laplace system given by − div ( | ∇ u | p − 2 ∇ u ) = div f . We show that f ∈ BMO implies | ∇ u | p − 2 ∇ u ∈...

Nonlinear Calderón–Zygmund theory | Elliptic systems | Campanato estimates | BMO estimates | Nonlinear CalderónZygmund theory | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | ELLIPTIC-SYSTEMS | Nonlinear Calderon-Zygmund theory | GRADIENT | Nonlinearity | Estimates | Regularity | Images | Constraining

Nonlinear Calderón–Zygmund theory | Elliptic systems | Campanato estimates | BMO estimates | Nonlinear CalderónZygmund theory | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | ELLIPTIC-SYSTEMS | Nonlinear Calderon-Zygmund theory | GRADIENT | Nonlinearity | Estimates | Regularity | Images | Constraining

Journal Article

Potential Analysis, ISSN 0926-2601, 10/2016, Volume 45, Issue 3, pp. 463 - 483

In this paper we present a Calderón-Zygmund approach for a large class of parabolic equations with pseudo-differential operators 𝒜 ( t ) $\mathcal {A}(t)$ of...

Geometry | Calderón-Zygmund approach | 35K30 | Potential Theory | Functional Analysis | Parabolic Pseudo-differential equations | 35B45 | 42B20 | 35S10 | Probability Theory and Stochastic Processes | L q ( L p )-estimate | Mathematics | estimate

Geometry | Calderón-Zygmund approach | 35K30 | Potential Theory | Functional Analysis | Parabolic Pseudo-differential equations | 35B45 | 42B20 | 35S10 | Probability Theory and Stochastic Processes | L q ( L p )-estimate | Mathematics | estimate

Journal Article

1996, ICASE/LaRC Series in Computational Science & Engineering, ISBN 9780195094237, 523

Wavelets are spatially localised functions whose amplitude drops off exponentially outside a small 'window'. They are used to magnify experimental or numerical...

Wavelets | Mathematics | Wavelets (Mathematics) | Harmonic analysis

Wavelets | Mathematics | Wavelets (Mathematics) | Harmonic analysis

eBook

Advances in Mathematics, ISSN 0001-8708, 12/2001, Volume 164, Issue 1, pp. 57 - 116

Let μ be a Radon measure on Rd which may be non-doubling. The only condition that μ must satisfy is μ(B(x, r))⩽Crn, for all x∈Rd, r>0, and for some fixed...

Calderón–Zygmund operators | T theorem | Littlewood–Paley theory | non-doubling measures | Calderó | Paley theory | Zygmund operators | Littlewood | Littlewood-Paley theory | Calderón-Zygmund operators | Non-doubling measures | MATHEMATICS | Littlewood Paley theory | Calderon Zygmund operators | CAUCHY

Calderón–Zygmund operators | T theorem | Littlewood–Paley theory | non-doubling measures | Calderó | Paley theory | Zygmund operators | Littlewood | Littlewood-Paley theory | Calderón-Zygmund operators | Non-doubling measures | MATHEMATICS | Littlewood Paley theory | Calderon Zygmund operators | CAUCHY

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 09/2014, Volume 106, pp. 70 - 85

We consider Calderón–Zygmund type estimates for the non-homogeneous p(⋅)-Laplacian system −div(|Du|p(⋅)−2Du)=−div(|G|p(⋅)−2G), where p is a variable exponent....

Nonlinear Calderón–Zygmund theory | Generalized Lebesgue and Sobolev spaces | Electrorheological fluids | Variable exponents | Nonlinear Calderón-Zygmund theory | MATHEMATICS, APPLIED | INTEGRABILITY | MAXIMAL-FUNCTION | EQUATIONS | Nonlinear Calderon-Zygmund theory | MATHEMATICS | REGULARITY | GROWTH | ELLIPTIC-SYSTEMS | LEBESGUE SPACES L-P(CENTER-DOT) | L-P SPACES | OPERATORS | FUNCTIONALS | Paper | Nonlinearity | Exponents | Intersections | Estimates

Nonlinear Calderón–Zygmund theory | Generalized Lebesgue and Sobolev spaces | Electrorheological fluids | Variable exponents | Nonlinear Calderón-Zygmund theory | MATHEMATICS, APPLIED | INTEGRABILITY | MAXIMAL-FUNCTION | EQUATIONS | Nonlinear Calderon-Zygmund theory | MATHEMATICS | REGULARITY | GROWTH | ELLIPTIC-SYSTEMS | LEBESGUE SPACES L-P(CENTER-DOT) | L-P SPACES | OPERATORS | FUNCTIONALS | Paper | Nonlinearity | Exponents | Intersections | Estimates

Journal Article

17.
Full Text
Global gradient estimates for general nonlinear parabolic equations in nonsmooth domains

Journal of Differential Equations, ISSN 0022-0396, 06/2013, Volume 254, Issue 11, pp. 4290 - 4326

We establish the natural Calderón–Zygmund theory for a nonlinear parabolic equation of p-Laplacian type in divergence form,(0.1)ut−diva(Du,x,t)=div(|F|p−2F)in...

Global estimate | Calderón–Zygmund theory | BMO nonlinearity | Reifenberg domain | Calderón-Zygmund theory | MATHEMATICS | INTEGRABILITY | REGULARITY | DIRICHLET PROBLEM | ORLICZ SPACES | COEFFICIENTS | SYSTEMS | ELLIPTIC-EQUATIONS | BMO NONLINEARITY

Global estimate | Calderón–Zygmund theory | BMO nonlinearity | Reifenberg domain | Calderón-Zygmund theory | MATHEMATICS | INTEGRABILITY | REGULARITY | DIRICHLET PROBLEM | ORLICZ SPACES | COEFFICIENTS | SYSTEMS | ELLIPTIC-EQUATIONS | BMO NONLINEARITY

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 05/2020, Volume 194, p. 111452

Nonlinear Potential theory aims at replicating the classical linear potential theory when nonlinear equations are considered. In recent years there has been a...

Regularity | Calderón–Zygmund theory | Elliptic equations | Nonlinear Potential Theory | LOCAL BEHAVIOR | MATHEMATICS, APPLIED | SUPERHARMONIC FUNCTIONS | PARABOLIC EQUATIONS | Calderon-Zygmund theory | BMO COEFFICIENTS | ZYGMUND THEORY | GRADIENT REGULARITY | HOLDER REGULARITY | MATHEMATICS | HARMONIC-FUNCTIONS | ELLIPTIC-EQUATIONS | WEAK SOLUTIONS

Regularity | Calderón–Zygmund theory | Elliptic equations | Nonlinear Potential Theory | LOCAL BEHAVIOR | MATHEMATICS, APPLIED | SUPERHARMONIC FUNCTIONS | PARABOLIC EQUATIONS | Calderon-Zygmund theory | BMO COEFFICIENTS | ZYGMUND THEORY | GRADIENT REGULARITY | HOLDER REGULARITY | MATHEMATICS | HARMONIC-FUNCTIONS | ELLIPTIC-EQUATIONS | WEAK SOLUTIONS

Journal Article