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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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https://hal.archives-ouvertes.fr/hal-03558491
Contributor : Sandrine Grellier Connect in order to contact the contributor
Submitted on : Tuesday, September 6, 2022 - 7:05:27 PM
Last modification on : Friday, September 9, 2022 - 3:31:54 AM

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  • HAL Id : hal-03558491, version 2
  • ARXIV : 2209.03595

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

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