Proceedings of the American Mathematical Society, ISSN 0002-9939, 04/2008, Volume 136, Issue 4, pp. 1237 - 1249

We establish the best possible bound on the norm of the Riesz transforms as operators in the weighted space L^p_{\mathbb{R}^n}(\omega) for 1 < p<\infty in...

Embeddings | Cubes | Dyadics | Fourier transformations | Mathematical constants | Mathematical functions | Mathematical inequalities | Children | Signatures | MATHEMATICS | MATHEMATICS, APPLIED | NORM INEQUALITIES | PLANE | DYADIC SHIFTS | HILBERT TRANSFORM | BELLMAN FUNCTIONS | OPERATORS

Embeddings | Cubes | Dyadics | Fourier transformations | Mathematical constants | Mathematical functions | Mathematical inequalities | Children | Signatures | MATHEMATICS | MATHEMATICS, APPLIED | NORM INEQUALITIES | PLANE | DYADIC SHIFTS | HILBERT TRANSFORM | BELLMAN FUNCTIONS | OPERATORS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 03/2016, Volume 270, Issue 5, pp. 1719 - 1743

Let W denote a matrix A2 weight. In this paper, we implement a scalar argument using the square function to deduce related bounds for vector-valued functions...

Hilbert transform | Square function | Matrix [formula omitted] weights | Haar multipliers | Matrix A | weights | Mathematics | Classical Analysis and ODEs

Hilbert transform | Square function | Matrix [formula omitted] weights | Haar multipliers | Matrix A | weights | Mathematics | Classical Analysis and ODEs

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 12/2019, Volume 582, pp. 452 - 466

We prove failure of the natural formulation of a matrix weighted bilinear Carleson embedding theorem, featuring a matrix–valued Carleson sequence as well as...

Matrix weight | Carleson embedding theorem | Bilinear embedding | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | MULTIPLIERS | HILBERT TRANSFORM | BELLMAN FUNCTIONS | Theorems | Redundancy | Dependence | Norms | Embedding | Failure | Weight

Matrix weight | Carleson embedding theorem | Bilinear embedding | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | MULTIPLIERS | HILBERT TRANSFORM | BELLMAN FUNCTIONS | Theorems | Redundancy | Dependence | Norms | Embedding | Failure | Weight

Journal Article

ANNALS OF PROBABILITY, ISSN 0091-1798, 03/2019, Volume 47, Issue 2, pp. 896 - 925

We prove optimal L-2 bounds for a pair of Hilbert space valued differentially subordinate martingales under a change of law. The change of law is given by a...

MARTINGALES | differential subordination | SHARP INEQUALITIES | RIESZ TRANSFORMS | NORM | BEURLING-AHLFORS | STATISTICS & PROBABILITY | Bellman function | HILBERT TRANSFORM | BELLMAN FUNCTIONS | Weight | L-P-BOUNDS

MARTINGALES | differential subordination | SHARP INEQUALITIES | RIESZ TRANSFORMS | NORM | BEURLING-AHLFORS | STATISTICS & PROBABILITY | Bellman function | HILBERT TRANSFORM | BELLMAN FUNCTIONS | Weight | L-P-BOUNDS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 03/2016, Volume 270, Issue 5, p. 1719

Let W denote a matrix A.sub.2 weight. In this paper, we implement a scalar argument using the square function to deduce related bounds for vector-valued...

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 03/2016, Volume 270, Issue 5, p. 1719

To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1016/j.jfa.2015.12.006 Let W...

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2017, Volume 318, pp. 279 - 306

We introduce the so called convex body valued sparse operators, which generalize the notion of sparse operators to the case of spaces of vector valued...

Matrix weighted maximal function | Matrix weights martingale transform | MATHEMATICS | HILBERT TRANSFORM | A WEIGHTS | OPERATORS

Matrix weighted maximal function | Matrix weights martingale transform | MATHEMATICS | HILBERT TRANSFORM | A WEIGHTS | OPERATORS

Journal Article

8.
Full Text
Second Order Riesz Transforms on Multiply–Connected Lie Groups and Processes with Jumps

Potential Analysis, ISSN 0926-2601, 11/2016, Volume 45, Issue 4, pp. 777 - 794

We study a class of combinations of second order Riesz transforms on Lie groups G = G x × G y $\mathbb {G}=\mathbb {G}_{x} \times \mathbb {G}_{y}$ that are...

Geometry | Potential Theory | Functional Analysis | MSC 22E30 | Probability Theory and Stochastic Processes | Riesz transform | Mathematics | Jump process | Lie group | Discrete group | MSC 60G75 | MSC 60G46 | MATHEMATICS | SHARP INEQUALITIES | SUBORDINATION | BOUNDS | MARTINGALE TRANSFORMS | BEURLING-AHLFORS | L-P

Geometry | Potential Theory | Functional Analysis | MSC 22E30 | Probability Theory and Stochastic Processes | Riesz transform | Mathematics | Jump process | Lie group | Discrete group | MSC 60G75 | MSC 60G46 | MATHEMATICS | SHARP INEQUALITIES | SUBORDINATION | BOUNDS | MARTINGALE TRANSFORMS | BEURLING-AHLFORS | L-P

Journal Article

Analysis and PDE, ISSN 2157-5045, 2016, Volume 9, Issue 5, pp. 1079 - 1113

We dominate nonintegral singular operators by adapted sparse operators and derive optimal norm estimates in weighted spaces. Our assumptions on the operators...

Weights | Singular operators | MATHEMATICS, APPLIED | INEQUALITIES | HARDY-SPACES | HAAR MULTIPLIERS | PARAPRODUCTS | HILBERT TRANSFORM | weights | ELLIPTIC-OPERATORS | INTEGRALS | MATHEMATICS | INFINITY-FUNCTIONAL-CALCULUS | MANIFOLDS | singular operators | DOMAINS

Weights | Singular operators | MATHEMATICS, APPLIED | INEQUALITIES | HARDY-SPACES | HAAR MULTIPLIERS | PARAPRODUCTS | HILBERT TRANSFORM | weights | ELLIPTIC-OPERATORS | INTEGRALS | MATHEMATICS | INFINITY-FUNCTIONAL-CALCULUS | MANIFOLDS | singular operators | DOMAINS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 09/2014, Volume 262, pp. 932 - 952

We show that multipliers of second order Riesz transforms on products of discrete abelian groups enjoy the estimate - 1, where = max{p, q} and p and q are...

Second order r iesz transforms | Discrete groups | MATHEMATICS | Second order Riesz transforms | INEQUALITIES | OPERATOR | MARTINGALE TRANSFORMS | Sharp L-p estimates | AHLFORS

Second order r iesz transforms | Discrete groups | MATHEMATICS | Second order Riesz transforms | INEQUALITIES | OPERATOR | MARTINGALE TRANSFORMS | Sharp L-p estimates | AHLFORS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 03/2016, Volume 291, pp. 24 - 58

We characterize Lp boundedness of iterated commutators of multiplication by a symbol function and tensor products of Riesz and Hilbert transforms. We obtain a...

Multi-parameter | BMO | Iterated commutator | Journé operator | Journe operator | MATHEMATICS | HARDY-SPACES | PARAPRODUCTS | PROOF | RIESZ COMMUTATORS | OPERATORS | ITERATED COMMUTATORS

Multi-parameter | BMO | Iterated commutator | Journé operator | Journe operator | MATHEMATICS | HARDY-SPACES | PARAPRODUCTS | PROOF | RIESZ COMMUTATORS | OPERATORS | ITERATED COMMUTATORS

Journal Article

Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 09/2017, Volume 34, Issue 5, pp. 1155 - 1180

We prove that a sharp regularity property (A∞) of parabolic measure for operators in certain time-varying domains is equivalent to a Carleson measure property...

BMO Dirichlet problem | Parabolic boundary value problem | [formula omitted] condition | condition | MATHEMATICS, APPLIED | DRIFT TERMS | A(infinity) condition | HEAT-EQUATION | LIPSCHITZ CYLINDERS | DIRICHLET PROBLEM | ELLIPTIC-EQUATIONS | DOMAINS | LAYER POTENTIALS

BMO Dirichlet problem | Parabolic boundary value problem | [formula omitted] condition | condition | MATHEMATICS, APPLIED | DRIFT TERMS | A(infinity) condition | HEAT-EQUATION | LIPSCHITZ CYLINDERS | DIRICHLET PROBLEM | ELLIPTIC-EQUATIONS | DOMAINS | LAYER POTENTIALS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 04/2014, Volume 266, Issue 8, pp. 5300 - 5320

We consider iterated commutators of multiplication by a symbol function and smooth Calderón–Zygmund operators, described by Fourier multipliers of homogeneity...

Hankel operator | Commutator | Product BMO | MATHEMATICS | COVERING LEMMA | SPACES | TERMS | HANKEL-OPERATORS | VARIABLES | Functional Analysis | Mathematics

Hankel operator | Commutator | Product BMO | MATHEMATICS | COVERING LEMMA | SPACES | TERMS | HANKEL-OPERATORS | VARIABLES | Functional Analysis | Mathematics

Journal Article

Bulletin des sciences mathématiques, ISSN 0007-4497, 07/2017, Volume 141, Issue 5, pp. 385 - 407

We show that the norm of the vector of Riesz transforms as operator in the weighted Lebesgue space Lω2 is bounded by a constant multiple of the first power of...

Riesz transforms | Weighted estimates | Bellman function | Background noise | MATHEMATICS, APPLIED | REAL VARIABLE CHARACTERIZATION | NORM INEQUALITIES | HILBERT TRANSFORM | SHARP ESTIMATE | 2-WEIGHT INEQUALITY | LEBESGUE SPACES | BELLMAN FUNCTIONS | OPERATORS | Mathematics

Riesz transforms | Weighted estimates | Bellman function | Background noise | MATHEMATICS, APPLIED | REAL VARIABLE CHARACTERIZATION | NORM INEQUALITIES | HILBERT TRANSFORM | SHARP ESTIMATE | 2-WEIGHT INEQUALITY | LEBESGUE SPACES | BELLMAN FUNCTIONS | OPERATORS | Mathematics

Journal Article

Mathematische Annalen, ISSN 0025-5831, 09/2010, Volume 348, Issue 1, pp. 127 - 141

Journal Article

Analysis and PDE, ISSN 2157-5045, 2018, Volume 11, Issue 7, pp. 1693 - 1740

We characterize the boundedness of the commutators [b, T] with biparameter Journe operators T in the two-weight, Bloom-type setting, and express the norms of...

Multiparameter harmonic analysis | Bounded mean oscillation | Weighted inequalities | Calderón-Zygmund operators | Journé operators | Weights | Singular integrals | Commutators | Little BMO | MATHEMATICS, APPLIED | little BMO | HANKEL-OPERATORS | weights | PRODUCT-SPACES | weighted inequalities | MATHEMATICS | Journe operators | commutators | bounded mean oscillation | multiparameter harmonic analysis | Calderon-Zygmund operators | singular integrals | SINGULAR-INTEGRALS

Multiparameter harmonic analysis | Bounded mean oscillation | Weighted inequalities | Calderón-Zygmund operators | Journé operators | Weights | Singular integrals | Commutators | Little BMO | MATHEMATICS, APPLIED | little BMO | HANKEL-OPERATORS | weights | PRODUCT-SPACES | weighted inequalities | MATHEMATICS | Journe operators | commutators | bounded mean oscillation | multiparameter harmonic analysis | Calderon-Zygmund operators | singular integrals | SINGULAR-INTEGRALS

Journal Article

COMPTES RENDUS MATHEMATIQUE, ISSN 1631-073X, 06/2014, Volume 352, Issue 6, pp. 503 - 506

We show that multipliers of second-order Riesz transforms on products of discrete Abelian groups enjoy the L-P estimate (p* - 1), where p* = max{p, q}, 1/p +...

MATHEMATICS

MATHEMATICS

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 04/2002, Volume 112, Issue 2, pp. 281 - 305

We establish borderline regularity for solutions of the Beltrami equation f(z) - muf((z) over bar) = 0 on the plane, where mu is a bounded measurable function,...

MARTINGALES | MATHEMATICS | SHARP INEQUALITIES | MAPPINGS | RIESZ TRANSFORMS | 35K05 | 47B38 | 42C15 | 42B20 | 30C62 | 47B35

MARTINGALES | MATHEMATICS | SHARP INEQUALITIES | MAPPINGS | RIESZ TRANSFORMS | 35K05 | 47B38 | 42C15 | 42B20 | 30C62 | 47B35

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 08/2007, Volume 249, Issue 2, pp. 372 - 392

We establish L -solvability for 1 < p < ∞ of the Dirichlet problem on Lipschitz domains with small Lipschitz constants for elliptic divergence and...

Dirichlet problem | Elliptic second order operators | Lipschitz domains

Dirichlet problem | Elliptic second order operators | Lipschitz domains

Journal Article

American Journal of Mathematics, ISSN 0002-9327, 6/2009, Volume 131, Issue 3, pp. 731 - 769

It is shown that product BMO of S.-Y. A. Chang and R. Fefferman, defined on the space , can be characterized by the multiparameter commutators of Riesz...

Tensors | Rectangles | Cubes | Coordinate systems | Fourier transformations | Polynomials | Mathematical vectors | Mathematical functions | Commutators | Hardy spaces | Riesz spaces | MATHEMATICS | COVERING LEMMA | BMO | OPERATORS | PRODUCT | Commutative law (Mathematics) | Transformations (Mathematics) | Research | Harmonic analysis | Algebraic group theory | Numerical analysis | Mathematics - Classical Analysis and ODEs

Tensors | Rectangles | Cubes | Coordinate systems | Fourier transformations | Polynomials | Mathematical vectors | Mathematical functions | Commutators | Hardy spaces | Riesz spaces | MATHEMATICS | COVERING LEMMA | BMO | OPERATORS | PRODUCT | Commutative law (Mathematics) | Transformations (Mathematics) | Research | Harmonic analysis | Algebraic group theory | Numerical analysis | Mathematics - Classical Analysis and ODEs

Journal Article

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