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Journal of functional analysis, ISSN 0022-1236, 2019, Volume 277, Issue 6, pp. 1639 - 1676
...=1nXj2 be the sub-Laplacian on G. The jth Riesz transform on G is defined by Rj:=Xj(−Δ)−12, 1≤j≤n. In this paper, we provide a concrete construction... 
Riesz transforms | Commutator | VMO space | Stratified Lie groups | MATHEMATICS | BOUNDEDNESS | INTEGRAL-OPERATORS | HOMOGENEOUS TYPE | HARDY SPACES
Journal Article
Advances in Mathematics, ISSN 0001-8708, 07/2012, Volume 230, Issue 4-6, pp. 2198 - 2234
Given a sequence of martingale differences, Burkholder found the sharp constant for the Lp-norm of the corresponding martingale transform... 
Ahlfors–Beurling transform | Monge–Ampère equation | Martingale | Riesz transform | Bellman function | Martingale transform | Perturbation | Monge-Ampère equation | Ahlfors-Beurling transform | MATHEMATICS | SHARP INEQUALITIES | Monge-Ampere equation | AHLFORS TRANSFORM
Journal Article
Memoirs of the American Mathematical Society, ISSN 0065-9266, 01/2017, Volume 245, Issue 1158, pp. 1 - 134
This monograph is devoted to the proof of two related results. The first one asserts that if mu is a Radon measure in R-d satisfying lim sup (r -> 0) mu(B(x,... 
Cauchy transform | Rectifiability | Square function | Density | MATHEMATICS | density | UNIFORM RECTIFIABILITY | DOUBLING MEASURES | SETS | RIESZ TRANSFORM | square function | ANALYTIC CAPACITY
Journal Article
Journal of Fourier Analysis and Applications, ISSN 1069-5869, 6/2018, Volume 24, Issue 3, pp. 699 - 718
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 12/2015, Volume 269, Issue 11, pp. 3402 - 3457
Journal Article
Signal Processing, ISSN 0165-1684, 05/2014, Volume 98, pp. 158 - 165
The fractional Fourier transform (FRFT), a generalization of the Fourier transform, has proven to be a powerful tool in optics and signal processing... 
Sampling theorem | Riesz bases | Function spaces | Truncation error | Fractional Fourier transform | DOMAIN | CONVERSION | TIME-FREQUENCY | RECONSTRUCTION | SHIFT-INVARIANT SPACES | SIGNALS | ENGINEERING, ELECTRICAL & ELECTRONIC | Electrical engineering | Analysis | Fourier transforms | Theorems | Function space | Signal processing | Derivation | Band theory | Truncation errors | Sampling
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 06/2020, Volume 148, Issue 6, pp. 2433 - 2446
We show that the centered discrete Hilbert transform on integers applied to a function can be written as the conditional expectation of a transform of stochastic integrals, where the stochastic... 
MARTINGALES | MATHEMATICS | MATHEMATICS, APPLIED | RIESZ TRANSFORMS | LIE-GROUPS | INEQUALITIES | ANALOGS | HARMONIC-ANALYSIS | DIFFERENTIAL SUBORDINATION | OPERATORS
Journal Article
Revista Matematica Iberoamericana, ISSN 0213-2230, 2017, Volume 33, Issue 3, pp. 749 - 788
We investigate the L-p-boundedness of the Riesz transform on Riemannian manifolds whose Ricci curvature has quadratic decay... 
Heat kernel | Riesz transform | Harmonic forms | INEQUALITIES | SPACES | NONCOMPACT RIEMANNIAN-MANIFOLDS | ELLIPTIC-OPERATORS | MATHEMATICS | VOLUME GROWTH | LOW-ENERGY | BOUNDS | RESOLVENT | heat kernel | harmonic forms | SCHRODINGER-OPERATORS
Journal Article
Journal of the European Mathematical Society, ISSN 1435-9855, 2018, Volume 20, Issue 3, pp. 529 - 595
We obtain dimension free estimates for noncommutative Riesz transforms associated to conditionally negative length functions on group von Neumann algebras... 
Dimension free estimates | Group von Neumann algebra | Hörmander-Mikhlin multiplier | Riesz transform | MATHEMATICS | MATHEMATICS, APPLIED | dimension free estimates | INEQUALITIES | THEOREM | ALGEBRA | Hormander-Mikhlin multiplier | group von Neumann algebra
Journal Article
Potential Analysis, ISSN 0926-2601, 10/2018, Volume 49, Issue 3, pp. 381 - 410
.... Under the strongly subcritical assumption on V, we study the L q boundedness of Riesz transform ∇ m L −1/2 for q ≤ 2 based on the off-diagonal estimates of semigroup e... 
Off-diagonal estimates | Higher order Schrödinger operator | L p - L q estimates | Probability Theory and Stochastic Processes | Riesz transform | Mathematics | 35J15 | Geometry | 42B35 | 42B25 | Potential Theory | Functional Analysis | 42B30 | estimates | MATHEMATICS | Higher order Schrodinger operator | WAVE | INEQUALITIES | GAUSSIAN BOUNDS | SPACES | HARDY | EQUATION | ELLIPTIC-OPERATORS | L-p-L-q estimates
Journal Article
Revista Matematica Iberoamericana, ISSN 0213-2230, 2014, Volume 30, Issue 2, pp. 477 - 522
...; notice that H is homogeneous of degree -2. We study the Riesz transform T = del H-1/2 and determine the precise range of p for which T is bounded on L-P(M... 
Metric cone | Riesz transform | Resolvent | Inverse square potential | Schrödinger operator | INEQUALITIES | SINGULARITIES | SPACES | CONICAL MANIFOLDS | inverse square potential | POTENTIALS | MATHEMATICS | LIE-GROUPS | POLYNOMIAL-GROWTH | LOW-ENERGY | EXPANSION | Schrodinger operator | resolvent
Journal Article
Journal of inequalities and applications, ISSN 1029-242X, 2019, Volume 2019, Issue 1, pp. 1 - 20
...}$. As applications, we obtain the HL1 $H^{1}_{\mathcal{L}}$-boundedness of Riesz transforms and the imaginary power related to L $\mathcal{L}$. 
Molecular decomposition | 42B35 | 47B38 | Hardy type space | Generalized Schrödinger operator | Analysis | Mathematics, general | Riesz transform | Mathematics | Applications of Mathematics | MATHEMATICS | Generalized Schrodinger operator | MATHEMATICS, APPLIED | Operators (mathematics) | Radon
Journal Article
DUKE MATHEMATICAL JOURNAL, ISSN 0012-7094, 05/2006, Volume 133, Issue 1, pp. 59 - 93
... > 0, each of which carries the standard metric. Our main result is that the Riesz transform oil M is bounded from L-p(M) -> L-p(M; T*M) for 1 < p... 
LAPLACIAN | MATHEMATICS | INEQUALITIES | SPACES | RESOLVENT | BOUNDS | VARIETIES | HEAT KERNEL | RIEMANNIAN-MANIFOLDS | Mathematics | Functional Analysis | Differential Geometry | Analysis of PDEs | 58J35 | 42B20 | 58J50
Journal Article
Journal of Fourier Analysis and Applications, ISSN 1069-5869, 6/2016, Volume 22, Issue 3, pp. 493 - 541
Journal Article
Integral Transforms and Special Functions, ISSN 1065-2469, 10/2017, Volume 28, Issue 10, pp. 751 - 771
In this paper we study the Riesz transforms related to the Weinstein operators . We develop for a theory that runs parallel to the one for the Euclidean Riesz Transform... 
Riesz transforms | spaces of homogeneous type | Calderón-Zygmund operators | Weinstein's operator | weights | MATHEMATICS | A(p) weights | MATHEMATICS, APPLIED | 42B20 | 26A33 | 42B10 | Calderon-Zygmund operators | Operators (mathematics)
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 2017, Volume 2017, Issue 1, pp. 1 - 17
In this paper, we consider the Riesz transform of higher order associated with the harmonic oscillator L = -Delta+|x|(2... 
Riesz transform | Hermite expansions | Littlewood-Paley g-function | Hardy space | MATHEMATICS | MATHEMATICS, APPLIED | REVERSE HOLDER INEQUALITY | HARDY-SPACES | BOUNDEDNESS | SCHRODINGER-OPERATORS | Transformations (mathematics) | 42C10 | 42B25 | Research
Journal Article
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