Besov and {T}riebel-{L}izorkin spaces associated with {L}aguerre expansions of {H}ermite type (Q682141)

In this paper homogeneous Besov and Triebel-Lizorkin spaces associated with multi-dimensional Laguerre function expansions of Hermite type with index \(\alpha \in [-1/2, \infty)^d \setminus (-1/2, 1/2)^d,\;d \geq 1\) are defined and investigated. To achive expected goals Schwartz type spaces on \(\mathbb{R}^{d}_{+}\) are introduced and then tempered type distributions are constructed. The author extends some former results for Hermite function expansions to Laguerre function expansions of Hermite type, using their idea on Calderon reproducing formula reproducing formula and molecular decomposition.