Strong continuity on Hardy spaces

Abstract

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

References in corpus (2)

• Gaussian heat kernel upper bounds via Phragmén-Lindelöf theorem
• Remarks on spectral multiplier theorems on Hardy spaces associated with semigroups of operators