English

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 H1H^1 (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 BMO\mathrm{BMO}-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