English

On the consequences of a Mihlin-H\"ormander functional calculus: maximal and square function estimates

Functional Analysis 2016-08-08 v1

Abstract

We prove that the existence of a Mihlin-H\"ormander functional calculus for an operator LL implies the boundedness on LpL^p of both the maximal operators and the continuous square functions build on spectral multipliers of L.L. The considered multiplier functions are finitely smooth and satisfy an integral condition at infinity. In particular multipliers of compact support are admitted.

Keywords

Cite

@article{arxiv.1507.08114,
  title  = {On the consequences of a Mihlin-H\"ormander functional calculus: maximal and square function estimates},
  author = {Błażej Wróbel},
  journal= {arXiv preprint arXiv:1507.08114},
  year   = {2016}
}
R2 v1 2026-06-22T10:21:28.998Z