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The Hilbert Transform on Rearrangement-Invariant Spaces

Published online by Cambridge University Press:  20 November 2018

D. W. Boyd
D. W. Boyd*
Affiliation:
University of Toronto
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 599 - 616
Copyright
Copyright © Canadian Mathematical Society 1967

References

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