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Preprints, Working Papers, ... Year : 2022

GLOBAL STEIN THEOREM ON HARDY SPACES

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 BM O.
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Dates and versions

hal-03558491 , version 1 (04-02-2022)
hal-03558491 , version 2 (06-09-2022)

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Aline Bonami, Sandrine Grellier, Benoit Sehba. GLOBAL STEIN THEOREM ON HARDY SPACES. 2022. ⟨hal-03558491v2⟩
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