The \(\rho \)-variation of the Hermitian Riesz transform

DOI10.1007/s10114-010-9122-3zbMath1206.42008OpenAlexW1995225233MaRDI QIDQ601916

José Luis Torrea, Alberto De La Torre, Francisco Javier Martín-Reyes, Raquel Crescimbeni

Publication date: 29 October 2010

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-010-9122-3

zbMATH Keywords

Hilbert transformweighted estimateoscillation-\(\rho\)-variation singular integral

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (18)

Oscillation and variation inequalities for the commutators of singular integrals with Lipschitz functions ⋮ \(L^p\)-boundedness properties of variation operators in the Schrödinger setting ⋮ Oscillation and variation inequalities for singular integrals and commutators on weighted Morrey spaces ⋮ Variation inequalities related to Schrödinger operators on Morrey spaces ⋮ Oscillation and variation for semigroups associated with Bessel operators ⋮ Variation operators for singular integrals and their commutators on weighted Morrey spaces and Sobolev spaces ⋮ Variation operators for semigroups and Riesz transforms acting on weighted \(L^p\) and BMO spaces in the Schrödinger setting ⋮ On weighted compactness of variation operators of commutators of Riesz transforms in the Schrödinger setting ⋮ Weighted oscillation and variation inequalities for singular integrals and commutators satisfying Hörmander type conditions ⋮ Oscillation and variation inequalities for the multilinear singular integrals related to Lipschitz functions ⋮ Variation operators for semigroups and Riesz transforms on \(BMO\) in the Schrödinger setting ⋮ Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces ⋮ Variation and oscillation inequalities for commutators in two-weight setting ⋮ Variation inequalities related to Schrödinger operators on weighted Morrey spaces ⋮ Weighted variation inequalities for singular integrals and commutators ⋮ Sparse domination and weighted inequalities for the \(\rho\)-variation of singular integrals and commutators ⋮ Variation operators on weighted Hardy and BMO spaces in the Schrödinger setting ⋮ Weighted estimates and compactness of variation operators

Cites Work

• Pointwise ergodic theorems for arithmetic sets. With an appendix on return-time sequences, jointly with Harry Furstenberg, Yitzhak Katznelson and Donald S. Ornstein
• Variation in probability, ergodic theory and analysis
• Poisson integrals and Riesz transforms for Hermite function expansions with weights.
• Oscillation and variation for the Hilbert transform
• Vector-valued extensions of operators related to the Ornstein-Uhlenbeck semigroup
• Dimension free estimates for the oscillation of Riesz transforms
• Oscillation and variation for the Gaussian Riesz transforms and Poisson integral
• HERMITE FUNCTION EXPANSIONS VERSUS HERMITE POLYNOMIAL EXPANSIONS
• Hermite Conjugate Expansions
• Unnamed Item

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