We study different Sobolev spaces associated with multidimensional Laguerre expansions.
To do this we establish an analogue of PA Meyer's multiplier theorem, prove some …

Riesz transforms and conjugate Poisson integrals for multi-dimensional Laguerre function
expansions of type α are defined and investigated. It is proved that for any multi-index …

We prove interior Harnack's inequalities for solutions of fractional nonlocal equations. Our
examples include fractional powers of divergence form elliptic operators with potentials …

On Riesz transforms for Laguerre expansions Page 1 Journal of Functional Analysis 215 (2004)
217–240 On Riesz transforms for Laguerre expansions Adam Nowak1 Instytut Matematyki …

arxiv:2110.03493v2 [math.CA] 28 Jul 2022 Page 1 VARIATION INEQUALITIES FOR RIESZ
TRANSFORMS AND POISSON SEMIGROUPS ASSOCIATED WITH LAGUERRE POLYNOMIAL …

We propose a unified approach to the theory of Riesz transforms and conjugacy in the
setting of multi-dimensional orthogonal expansions. The scheme is supported by numerous …

In this paper we study the boundedness of spectral multipliers associated to the
multidimensional Laguerre operator. It is well known that, for special values of α, the …

Riesz transforms and conjugate Poisson integrals for multi-dimensional Laguerre function
expansions of Hermite type with index α are defined and investigated. It is proved that for …

In this paper we introduce the atomic Hardy space H 1 ((0,∞), γ α) associated with the non-
doubling probability measure d γ α (x)= 2 x 2 α+ 1 Γ (α+ 1) ex 2 dx on (0,∞), for α>-1 2. We …

We define Riesz transforms and conjugate Poisson integrals associated with multi-
dimensional Jacobi expansions. Under a slight restriction on the type parameters, we prove …