Square functions in the Hermite setting for functions with values in UMD spaces

DOI10.1007/s10231-013-0335-9zbMath1312.46047arXiv1203.1480OpenAlexW2076041885MaRDI QIDQ466954

Jezabel Curbelo, J. Carlos Fariña, Alejandro J. Castro, Jorge J. Betancor, Lourdes Rodríguez-Mesa

Publication date: 31 October 2014

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.1480

zbMATH Keywords

Littlewood-Paley \(g\)-functions\(\gamma\)-radonifying operatorsUMD Banach spacesHermite operator

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Spaces of vector- and operator-valued functions (46E40) Groups and semigroups of linear operators (47D03)

Related Items (13)

Square functions and spectral multipliers for Bessel operators in UMD spaces ⋮ Conical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spaces ⋮ Maximal operators, Littlewood-Paley functions and variation operators associated with nonsymmetric Ornstein-Uhlenbeck operators ⋮ Littlewood-Paley-Stein theory and Banach spaces in the inverse Gaussian setting ⋮ The Hardy-Littlewood property and maximal operators associated with the inverse Gauss measure ⋮ Variation inequalities for Riesz transforms and Poisson semigroups associated with Laguerre polynomial expansions ⋮ Vector valued multivariate spectral multipliers, Littlewood-Paley functions, and Sobolev spaces in the Hermite setting ⋮ The fractional Bessel equation in Hölder spaces ⋮ UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces ⋮ UMD Banach spaces and square functions associated with heat semigroups for Schrödinger, Hermite and Laguerre operators ⋮ Variation operators for semigroups associated with Fourier-Bessel expansions ⋮ Variation and oscillation for harmonic operators in the inverse Gaussian setting ⋮ Discrete harmonic analysis associated with ultraspherical expansions

Cites Work

• Unnamed Item
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• Lusin type and cotype for Laguerre \(g\)-functions
• Fractional square functions and potential spaces
• Some remarks on Banach spaces in which martingale difference sequences are unconditional
• Sobolev spaces associated to the harmonic oscillator
• Riesz transform and \(g\)-function associated with Bessel operators and their appropriate Banach spaces
• Littlewood-Paley-Stein theory for semigroups in UMD spaces
• The Banach space-valued BMO, Carleson's condition, and paraproducts
• Calderón-Zygmund theory for operator-valued kernels
• Poisson integrals and Riesz transforms for Hermite function expansions with weights.
• Higher order Riesz transforms, fractional derivatives, and Sobolev spaces for Laguerre expansions
• Vector-valued extensions of operators related to the Ornstein-Uhlenbeck semigroup
• On g-functions for Hermite function expansions
• A semigroup approach to stochastic delay equations in spaces of continuous functions
• Transference between Laguerre and Hermite settings
• Vector-valued Littlewood--Paley--Stein theory for semigroups
• What is a Sobolev space for the Laguerre function systems?
• vector-valued singular integrals and maximal functions on spaces of homogeneous type
• Littlewood-Paley theory for functions with values in uniformly convex spaces
• The Mehler Maximal Function: a Geometric Proof of the Weak Type 1
• Boundedness of Littlewood-Paley g-functions of higher order associated with the Ornstein-Uhlenbeck semigroup
• A General Multiplier Theorem
• Fractional vector-valued Littlewood–Paley–Stein theory for semigroups
• Wavelet transform for functions with values in UMD spaces
• HERMITE FUNCTION EXPANSIONS VERSUS HERMITE POLYNOMIAL EXPANSIONS
• Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)

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