On Lusin's area integrals andg-functions in certain Dunkl and Laguerre settings

DOI10.1002/MANA.201100096zbMath1252.42028arXiv1011.0898OpenAlexW2962908146MaRDI QIDQ2909663

Tomasz Zachary Szarek

Publication date: 6 September 2012

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.0898

zbMATH Keywords

\(g\)-functionCalderón-Zygmund operatorLaguerre expansions of convolution typesquare functionLaguerre semigroup\(A_{p}\) weightgeneralized Hermite expansionsDunkl's harmonic oscillatorLusin's area integral

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10)

Related Items (5)

On harmonic analysis operators in Laguerre-Dunkl and Laguerre-symmetrized settings ⋮ Lusin area integrals related to Jacobi expansions ⋮ Calderón-Zygmund operators in the Bessel setting for all possible type indices ⋮ Calderón-Zygmund operators related to Laguerre function expansions of convolution type ⋮ On fundamental harmonic analysis operators in certain Dunkl and Bessel settings

Cites Work

• Area Littlewood-Paley functions associated with Hermite and Laguerre operators
• Littlewood-Paley-Stein type square functions based on Laguerre semigroups
• Riesz transforms for the dunkl harmonic oscillator
• Poisson integrals and Riesz transforms for Hermite function expansions with weights.
• \(L^p\)-dimension free boundedness for Riesz transforms associated to Hermite functions
• Functional calculus for the Laguerre operator
• On g-functions for Hermite function expansions
• Riesz transforms for multi-dimensional Laguerre function expansions
• Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates
• Heat-diffusion and Poisson integrals for Laguerre and special Hermite expansions on weighted L^pspaces
• Mean Convergence of Expansions in Laguerre and Hermite Series
• Mean Convergence of Hermite and Laguerre Series. I

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