Hardy-Rellich Type Inequalities Associated with Dunkl Operators*

Citation:

Li TANG.Hardy-Rellich Type Inequalities Associated with Dunkl Operators*[J].Chinese Annals of Mathematics B,2022,43(2):281~294
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Authors:

Li TANG;

Foundation:

National Natural Science Foundation of China (Nos. 11771395,12071431).
Abstract: In this paper, the authors obtain the Dunkl analogy of classical Lp Hardy inequality for p>N+2γ with sharp constant (\p-N-2γ\p)p, where 2γ is the degree of weight function associated with Dunkl operators, and Lp Hardy inequalities with distant function in some G-invariant domains. Moreover they prove two Hardy-Rellich type inequalities for Dunkl operators.

Keywords:

Hardy inequalities, Hardy-Rellich inequalities, Best constant, Dunkl operators

Classification:

26D10, 42B37, 20F55
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