The Hilbert Transform on Rearrangement-Invariant Spaces
Author:
- D. W. BoydDBD. W. Boyd
- 1 January 1967
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 19, 599-616
Abstract
The purpose of this paper is to investigate conditions under which the Hilbert transform defines a bounded linear operator from a given function space into itself. The spaces with which we deal have the property of rearrangement-invariance which is defined in §1. This class of spaces includes the Lebesgue, Orlicz, and Lorentz spaces.Keywords
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