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arXiv · 1811.11118

Sobolev-Type Inequalities for Dunkl Operators

Andrei Velicu
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Abstract

In this paper we study the Sobolev inequality in the Dunkl setting using two new approaches which provide a simpler elementary proof of the classical case $p=2$, as well as an extension to the coefficient $p=1$ that was previously unknown. We also find estimates of the sharp constants for the Sobolev inequality for Dunkl gradient. Related inequalities and some improvements are also considered (Nash inequality, Besov space embeddings).

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Andrei Velicu. 2019-03-18. Sobolev-Type Inequalities for Dunkl Operators. https://arxiv.org/abs/1811.11118

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