Some remarks on the Banach space valued Hilbert transform
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 \(L_ p(0,1)\).
boundedness of the Banach space valued Hilbert transform
scientific article; zbMATH DE number 60867