A Note on Hardy Spaces and Bounded Operators
Classical Analysis and ODEs
2015-03-03 v2
Abstract
In this note we show that if f belongs to Hp(Rn)\capLs(Rn), where 0 < p <= 1 < s < 1, then there exists a (p;infinite)-atomic decomposition which converges to f in Ls(Rn). From this fact, we prove that a bounded operator T on Ls(Rn) can be extended to a bounded operator from Hp(Rn) into Lp(Rn) if and only if T is bounded uniformly in Lp norm on all (p;infinite)-atoms. A similar result is also obtained from Hp(Rn) into Hp(Rn).
Cite
@article{arxiv.1502.07542,
title = {A Note on Hardy Spaces and Bounded Operators},
author = {Pablo Rocha},
journal= {arXiv preprint arXiv:1502.07542},
year = {2015}
}