The Hardy and Bellman transforms of the spaces \(H^1\) and BMO
type: Item
instance of: scholarly article
title: The Hardy and Bellman transforms of the spaces \(H^1\) and BMO
zbMATH Open document ID: 0922.42007
DOI: 10.1007/BF02317792
published in: Mathematical Notes
publication date: 1999-09-21T00:00:00Z
review text: Hardy transform associates to a function a trigonometric series in which the \(n\)-th coefficients are means of the corresponding coefficients of the function. Bellman transform is the adjoint to Hardy transform. The author proves that the Hardy transform is bounded on \(H^1(T)\) and unbounded on \(\text{BMO}(T)\), and so the Bellman transform is bounded on \(\text{BMO}(T)\) and unbounded on \(H^1(T)\). This continues the old results about boundedness of both Hardy and Bellman transforms on \(L^p\), \(1<p<\infty\).
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 1262574
zbMATH Keywords: Hardy transform
zbMATH Keywords: Bellman transform
zbMATH Keywords: BMO bounded operator
zbMATH Keywords: \(H^1\) bounded operator
author: Boris Golubov
reviewed by: Maria Roginskaya
MaRDI profile type: Publication
cites work: A note on a theorem of Hardy on Fourier constants
cites work: On functions of bounded mean oscillation
cites work: Q3756738
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description: scientific article; zbMATH DE number 1262574