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arXiv · 1703.06830

Positive $L^p$-bounded Dunkl-type generalized translation operator and its applications

D. V. Gorbachev·V. I. Ivanov·S. Yu. Tikhonov
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Abstract

We prove that the spherical mean value of the Dunkl-type generalized translation operator $\tau^y$ is a positive $L^p$-bounded generalized translation operator $T^t$. As application, we prove the Young inequality for a convolution defined by $T^t$, the $L^p$-boundedness of $\tau^y$ on a radial functions for $p>2$, the $L^p$-boundedness of the Riesz potential for the Dunkl transform and direct and inverse theorems of approximation theory in $L^p$-spaces with the Dunkl weight.

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D. V. Gorbachev, V. I. Ivanov, S. Yu. Tikhonov. 2017-03-20. Positive $L^p$-bounded Dunkl-type generalized translation operator and its applications. https://arxiv.org/abs/1703.06830

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