English

Weighted norm inequalities for generalized Fourier-type transforms and applications

Classical Analysis and ODEs 2018-12-06 v1

Abstract

We obtain necessary and sufficient conditions on weights for the generalized Fourier-type transforms to be bounded between weighted LpLqL^p-L^q spaces. As an important example, we investigate transforms with kernel of power type, as for instance the sine, Hankel or Hα\mathscr{H}_\alpha transforms. The obtained necessary and sufficient conditions are given in terms of weights, but not in terms of their decreasing rearrangements, as in several previous investigations.

Keywords

Cite

@article{arxiv.1812.01928,
  title  = {Weighted norm inequalities for generalized Fourier-type transforms and applications},
  author = {A. Debernardi},
  journal= {arXiv preprint arXiv:1812.01928},
  year   = {2018}
}
R2 v1 2026-06-23T06:32:32.128Z