Endpoint estimates for harmonic analysis operators associated with Laguerre polynomial expansions

2022/10/26 by Jorge J. Betancor, Estefanía Dalmasso, Betancor, Jorge J. +5
Mathematics · #42B15 #42B20 #42B25 #42B35 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2210.14394

openalex publication_date 2022/10/26 · openalex created_date 2022/11/02 · openalex updated_date 2026/07/28

Abstract

In this paper we give a criterion to prove boundedness results for several operators from H¹((0,∞),γ_α) to L¹((0,∞),γ_α) and also from L^∞((0,∞),γ_α) to \BMO((0,∞),γ_α), with respect to the probability measure dγ_α(x)=(2)/(Γ(α+1)) x^2α+1 e^-x2 dx on (0,∞) when α>-\frac12. We shall apply it to establish endpoint estimates for Riesz transforms, maximal operators, Littlewood-Paley functions, multipliers of Laplace transform type, fractional integrals and variation operators in the Laguerre setting.

Related

• Harmonic analysis operators associated with Laguerre polynomial expansions on variable Lebesgue spaces
• BLO spaces associated with Laguerre polynomials expansions
• Maximal function characterization of Hardy spaces related to Laguerre polynomial expansions
• Multipliers of Laplace Transform Type for Laguerre and Hermite Expansions
• Variation inequalities for Riesz transforms and Poisson semigroups associated with Laguerre polynomial expansions