This article is cited in 10 papers

Papers published in the English version of the journal

Fractional Smoothness in $L^p$ with Dunkl Weight and Its Applications

D. V. Gorbachev, V. I. Ivanov

Tula State University, Tula, 300012 Russia

Abstract: We define a fractional power of the Dunkl Laplacian, a fractional modulus of smoothness, and a fractional $K$-functional on $L^p$-spaces with Dunkl weight. As an application, we extend our previous results and prove direct and inverse theorems of approximation theory and some inequalities for entire functions of spherical exponential type in the fractional setting.

Keywords: Dunkl transform, generalized translation operator, convolution, Dunkl Laplacian, modulus of smoothness, $K$-functional.

Received: 13.03.2019

Language: English

 English version: Mathematical Notes, 2019, 106:4, 537–561

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