Strong continuity on Hardy spaces

TL;DR

This paper establishes the strong continuity of spectral multiplier operators on Hardy spaces, including heat, Poisson, and imaginary power groups, expanding understanding of operator behavior in harmonic analysis.

Contribution

It proves strong continuity of spectral multipliers on Hardy spaces, covering key operators like heat, Poisson, and imaginary powers, for the first time in this context.

Findings

Spectral multipliers are strongly continuous on Hardy spaces.

Includes heat and Poisson semigroups as special cases.

Results extend the theory of operator continuity in harmonic analysis.

Abstract

We prove the strong continuity of spectral multiplier operators associated with dilations of certain functions on the general Hardy space $H^1_L$ introduced by Hofmann, Lu, Mitrea, Mitrea, Yan. Our results include the heat and Poisson semigroups as well as the group of imaginary powers.