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Sharp approximation theorems in the Dunkl setting | | D.V. Gorbachev
; V.I. Ivanov
; S.Yu. Tikhonov
; | | Date: |
8 Dec 2019 | | Abstract: | In this paper we study direct and inverse approximation inequalities in
$L^{p}(mathbb{R}^{d})$, $1<p<infty$, with the Dunkl weight. We obtain these
estimates in their sharp form substantially improving known results. Moreover,
we establish new estimates of the modulus of smoothness of a function $f$ via
the fractional powers of the Dunkl Laplacian of approximants of $f$. Needed
Pitt-type estimates for Dunkl transform are obtained as well as the Lebesgue
type estimate for moduli of smoothness. | | Source: | arXiv, 1912.3743 | | Services: | Forum | Review | PDF | Favorites | |
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