A multi-parameter Hardy type inequality
Functional Analysis
2020-10-07 v2
Abstract
This note contains two simple observations. First, by the weak factorization of product (Ferguson--Lacey, Lacey--Terwilleger), we obtain a multi-parameter analogue of Hardy's inequality. Second, as a dual statement, the Fourier transform of an essentially bounded function belongs to a certain product -Sobolev space.
Keywords
Cite
@article{arxiv.1912.08023,
title = {A multi-parameter Hardy type inequality},
author = {Eskil Rydhe},
journal= {arXiv preprint arXiv:1912.08023},
year = {2020}
}
Comments
The original proof of the Ferguson--Lacey theorem contains a serious error. Although my paper describes how to circumvent the use of the Ferguson--Lacey result, the associated revisions to make this a proper and correct paper are beyond my current schedule. Until I've had time to make a proper revision, I will withdraw the paper