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arXiv · 1809.08039

Besov and Triebel-Lizorkin spaces associated with Laguerre expansions of Hermite type

Paweł Plewa
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Abstract

Homogeneous Besov and Triebel-Lizorkin spaces associated with multi-dimensional Laguerre function expansions of Hermite type with index $α\in [-1/2,\infty)^d\backslash (-1/2,1/2)^d$, $d\geq 1$, are defined and investigated. To achieve expected goals Schwartz type spaces on $R^d_+$ are introduced and then tempered type distributions are constructed. Also, ideas from a recent paper of Bui and Duong on Besov and Triebel-Lizorkin spaces associated with Hermite functions expansions are used. This means, in particular, using molecular decomposition and an appropriate form of a Calderón reproducing formula.

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Paweł Plewa. 2018-09-21. Besov and Triebel-Lizorkin spaces associated with Laguerre expansions of Hermite type. https://doi.org/10.1007/s10474-017-0747-x

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