Classes of operators on weighted function spaces in Dunkl analysis
Analysis of PDEs
2013-11-05 v2
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.
Cite
@article{arxiv.1305.4394,
title = {Classes of operators on weighted function spaces in Dunkl analysis},
author = {Chokri Abdelkefi and Mongi Rachdi},
journal= {arXiv preprint arXiv:1305.4394},
year = {2013}
}
Comments
17 pages. arXiv admin note: substantial text overlap with arXiv:1301.6267, arXiv:1208.5034