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Convolution with Odd Kernels Having a Tempered Singularity

Published online by Cambridge University Press:  20 November 2018

R. A. Kerman
R. A. Kerman*
Affiliation:
Department of Mathematics, Brock University, St. Catharines, Ontario, L2S 3A1
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Abstract

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Suppose b(t) decreases to 0 on [1, ∞). Define the singular integral operator Cb at periodic f of period 1 in L1 (T),T = ( - 1 / 2, 1/2), by

Then, for a large class of b one has the rearrangement inequality

This inequality is used to construct a rearrangement invariant function space X corresponding to a given such space Y so that Cb maps X into Y.

Keywords

42A5046E30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 1 , 01 March 1988 , pp. 3 - 12
Copyright
Copyright © Canadian Mathematical Society 1988

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