Year: 2013
Type: preprint
Abstract: For indices p and q, 1 < p <= q < infini and a linear operator L satisfying some weak-type boundedness conditions on suitable function spaces, we give in the Dunkl setting sufficient conditions on nonnegative pairs of weight functions to obtain weighted norm inequalities for the operator L. We apply our results to obtain weighted (Lp, Lq) boundedness of the Riesz potentials and of the related fractional maximal operators for the Dunkl transform. Finally, we prove a weighted generalized Sobolev inequality.
Source: arXiv (Cornell University)
Authors: Abdelkefi, Chokri, Rachdi, Mongi
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1782250786