Lusin type and cotype for Laguerre \(g\)-functions

DOI10.1007/s11856-011-0021-9zbMath1222.46011OpenAlexW2093941986MaRDI QIDQ532600

Alejandro Sanabria, Jorge J. Betancor, Lourdes Rodríguez-Mesa, José Luis Torrea, J. Carlos Fariña

Publication date: 5 May 2011

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11856-011-0021-9

zbMATH Keywords

semigroup\(g\)-functionHermite differential operatorLaguerre differential operatorLusin cotypeLusin type

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Groups and semigroups of linear operators (47D03) Probabilistic methods in Banach space theory (46B09)

Related Items

Estimates for vector-valued holomorphic functions and Littlewood–Paley–Stein theory, \(\gamma \)-Radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces, Littlewood-Paley-Stein theory and Banach spaces in the inverse Gaussian setting, UMD Banach spaces and the maximal regularity for the square root of several operators, Littlewood-Paley-Stein type square functions based on Laguerre semigroups, Square functions in the Hermite setting for functions with values in UMD spaces, Vector valued multivariate spectral multipliers, Littlewood-Paley functions, and Sobolev spaces in the Hermite setting, Area Littlewood-Paley functions associated with Hermite and Laguerre operators, Uniformly convex and smooth Banach spaces and \(L^p\)-boundedness properties of Littlewood-Paley and area functions associated with semigroups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• BMO results for operators associated to Hermite expansions
• Riesz transform and \(g\)-function associated with Bessel operators and their appropriate Banach spaces
• A sharp weighted transplantation theorem for Laguerre function expansions
• Riesz transforms and conjugacy for Laguerre function expansions of Hermite type
• Power weighted \(L^p\) -inequalities for Laguerre-Riesz transforms
• Weak type \((1,1)\) estimates of the maximal function for the Laguerre semigroup in finite dimensions
• Martingales with values in uniformly convex spaces
• Poisson integrals and Riesz transforms for Hermite function expansions with weights.
• Higher order Riesz transforms, fractional derivatives, and Sobolev spaces for Laguerre expansions
• Transference between Laguerre and Hermite settings
• Vector-valued Littlewood--Paley--Stein theory for semigroups
• Heat-diffusion maximal operators for Laguerre semigroups with negative parameters
• Weighted norm inequalities for heat-diffusion Laguerre's semigroups
• Littlewood-Paley theory for functions with values in uniformly convex spaces
• Heat-diffusion and Poisson integrals for Laguerre and special Hermite expansions on weighted L^pspaces
• Riesz transforms and g-function for Laguerre expansions
• Hermite Conjugate Expansions
• Conjugate Functions for Laguerre Expansions