Bj\"ork-Sj\"olin condition for strongly singular convolution operators on graded Lie groups
Functional Analysis
2022-09-13 v3 Analysis of PDEs
Representation Theory
Abstract
In this work we extend the -Bj\"ork-Sj\"olin theory of strongly singular convolution operators to arbitrary graded Lie groups. Our criteria are presented in terms of the oscillating H\"ormander condition due to Bj\"ork and Sj\"olin of the kernel of the operator, and the decay of its group Fourier transform is measured in terms of the infinitesimal representation of an arbitrary Rockland operator. The historical result by Bj\"ork and Sj\"olin is re-obtained in the case of the Euclidean space.
Keywords
Cite
@article{arxiv.2205.03456,
title = {Bj\"ork-Sj\"olin condition for strongly singular convolution operators on graded Lie groups},
author = {Duván Cardona and Michael Ruzhansky},
journal= {arXiv preprint arXiv:2205.03456},
year = {2022}
}
Comments
22 Pages. arXiv admin note: text overlap with arXiv:2201.12881