Riesz Potential and Maximal Function for Dunkl transform

Riesz Potential and Maximal Function for Dunkl transform

We study weighted ( L p , L q )-boundedness properties of Riesz potentials and fractional maximal functions for the Dunkl transform. In particular, we obtain the weighted Hardy–Littlewood–Sobolev type inequality and weighted week ( L 1 , L q ) estimate. We find a sharp constant in the weighted L p -...

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Veröffentlicht in:Potential analysis 2021-12, Vol.55 (4), p.513-538
Hauptverfasser: Gorbachev, D. V., Ivanov, V. I., Tikhonov, S. Yu
Format: Artikel
Sprache:eng
Schlagworte:
Functional Analysis
Geometry
Mathematics
Mathematics and Statistics
Physical Sciences
Potential Theory
Probability Theory and Stochastic Processes
Science & Technology
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Zusammenfassung:We study weighted ( L p , L q )-boundedness properties of Riesz potentials and fractional maximal functions for the Dunkl transform. In particular, we obtain the weighted Hardy–Littlewood–Sobolev type inequality and weighted week ( L 1 , L q ) estimate. We find a sharp constant in the weighted L p -inequality, generalizing the results of W. Beckner and S. Samko.
ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-020-09867-z