@article{ace510a81a00485ea5b45de7cf0a887f,
title = "REMARK ON SINGULAR INTEGRAL OPERATORS OF CONVOLUTION TYPE ON REARRANGEMENT-INVARIANT BANACH FUNCTION SPACES",
abstract = "We prove that nondegenerate singular integral operators of convolution type are bounded on a rearrangement-invariant Banach function space X(Rd) if and only if its Boyd indices are nontrivial, extending the result by David Boyd (1966) for the Hilbert transform.",
keywords = "Boyd indices, Calder{\'o}n-Zygmund singular integral operators of convolution type, rearrangement-invariant Banach function spaces",
author = "Oleksiy Karlovych and Eugene Shargorodsky",
note = "Funding Information: info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT# info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F00297%2F2020/PT# Mathematical Reviews subject classification: Primary: 42B20, 46E30. Key words: Calder{\'o}n-Zygmund singular integral operators of convolution type, rearrangement-invariant Banach function spaces, Boyd indices. Received by the editors August 21, 2022 Communicated by: Andrei K. Lerner Publisher Copyright: {\textcopyright} 2023 Michigan State University Press. All rights reserved.",
year = "2023",
doi = "10.14321/realanalexch.48.1.1661058123",
language = "English",
volume = "48",
pages = "139--148",
journal = "Real Analysis Exchange",
issn = "0147-1937",
publisher = "Michigan State University Press",
number = "1",
}