Global Stein Theorem on Hardy spaces
Classical Analysis and ODEs
2025-06-23 v2
Abstract
Let f be an integrable function which has integral 0 on R n. What is the largest condition on |f | that guarantees that f is in the Hardy space H 1 (R n)? When f is compactly supported, it is well-known that it is necessary and sufficient that |f | belongs to L log L(R n). We are interested here in conditions at . We do so for H 1 (R n), as well as for the Hardy space H log (R n) which appears in the study of pointwise products of functions in H 1 (R n) and in its dual BMO.
Keywords
Cite
@article{arxiv.2209.03595,
title = {Global Stein Theorem on Hardy spaces},
author = {Aline Bonami and Sandrine Grellier and Benoit Sehba},
journal= {arXiv preprint arXiv:2209.03595},
year = {2025}
}