Strong continuity on Hardy spaces
  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. 
Jacek Dziuba\'nski, B{\l}a\.zej Wr\'obel
math.FA