Some remarks on the Banach space valued Hilbert transform (Q1192452)
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scientific article; zbMATH DE number 60867
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some remarks on the Banach space valued Hilbert transform |
scientific article; zbMATH DE number 60867 |
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Some remarks on the Banach space valued Hilbert transform (English)
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27 September 1992
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The authors give an elementary proof of the boundedness of the Banach space valued Hilbert transform for the spaces \(L_ p(\Omega,L_ q(\Sigma))\), where \(1<p,q<\infty\) and \(\Omega\), \(\Sigma\) are \(\sigma\)- finite measure spaces. The main step is an extension to the vector-valued case of a proof, due to Bochner, of the continuity of the Riesz projection in \(L_ p(0,1)\).
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boundedness of the Banach space valued Hilbert transform
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continuity of the Riesz projection
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