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https://doi.org/10.1...arrow_drop_down

https://doi.org/10.1007/978-1-...

Part of book or chapter of book . 1997 . Peer-reviewed

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H1 and BMO

Name: H1 and BMO
Creator: Mats Andersson

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Other literature type 01 Jan 1997Publisher:Springer New York

Authors: Mats Andersson;

doi: 10.1007/978-1-4612-4042-6_10

H1 and BMO

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Abstract

Recall from Ch. 6 that a function u on T is in L p (T) if and only if its Hubert transform Hu is. By virtue of (2.8) in Ch. 6, we can define the Hubert transform even for u ∈ L1(T) as a formal Fourier series; in general, it will not belong to L1(T) but merely be a distribution; cf. Remark 2.1 in Ch. 6. More precisely, Hu is in L1(T) if and only if u = Re f* for some f ∈ H1.

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Chalmers University of Technology
Sweden

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