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Remark on singular integral operators of convolution type on rearrangement-invariant Banach function spaces

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Eugene Shargorodsky, Oleksiy Karlovych

Original languageEnglish
JournalReal Analysis Exchange
Accepted/In press31 Aug 2022

King's Authors

Abstract

We prove that nondegenerate singular integral operators of convolution type are bounded on a rearrangement-invariant Banach function space $X(\mathbb{R}^d)$ if and only if its Boyd indices are nontrivial, extending the result by David Boyd (1966) for the Hilbert transform.

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