A Note on UMD Spaces and Transference in Vector-valued Function Spaces
Functional Analysis
2008-02-03 v2
Abstract
We introduce the notion of an ACF space, that is, a space for which a generalized version of M. Riesz's theorem for conjugate functions with values in the Banach space is bounded. We use transference to prove that spaces for which the Hilbert transform is bounded, i\.e\. , are ACF spaces. We then show that Bourgain's proof of is a consequence of this result.
Keywords
Cite
@article{arxiv.math/9406218,
title = {A Note on UMD Spaces and Transference in Vector-valued Function Spaces},
author = {N. Asmar and B. Kelly and Stephen J. Montgomery-Smith},
journal= {arXiv preprint arXiv:math/9406218},
year = {2008}
}