Abstract
We investigate Laplace transform type and Laplace-Stieltjes type multipliers associated to the multi–dimensional Laguerre function expansions of Hermite type. We prove that, under the assumption α i ≥ −1/2, α i ∉ (−1/2, 1/2), these operators are Calderón-Zygmund operators. Consequently, their mapping properties follow by the general theory.
Highlights
The study of multipliers for various Laguerre systems began with the paper of Dlugosz [3]
Recent papers dealing with Laplace transform type multipliers for the same Laguerre system are the articles by Drelichman, Duran, de Napoli [4], and Szarek [18]
Laplace transform type multipliers have been considered for continuous orthogonal systems, see for instance Betancor, Martınez and Rodrıguez-Mesa [1]
Summary
The study of multipliers for various Laguerre systems began with the paper of Dlugosz [3]. Recent papers dealing with Laplace transform type multipliers for the same Laguerre system are the articles by Drelichman, Duran, de Napoli [4], and Szarek [18]. These types of multipliers, again for Laguerre expansions of convolution type, were studied by Nowak and Szarek in [12]. In this article we study Laplace transform type and Laplace-Stieltjes type multipliers associated with Laguerre function expansions of Hermite type (see Section 2 for the definitions). To treat Laplace transform type multipliers we use methods developed
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