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arXiv · 2209.03595

Global Stein Theorem on Hardy spaces

Aline Bonami·Sandrine Grellier·Benoit Sehba
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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 $\infty$. 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.

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Aline Bonami, Sandrine Grellier, Benoit Sehba. 2022-09-08. Global Stein Theorem on Hardy spaces. https://arxiv.org/abs/2209.03595

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