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A multiplier relation for Calderón-Zygmund operators on $L^{1}(\mathbb{R}^{n})$


Author: Jonathan Bennett
Journal: Proc. Amer. Math. Soc. 127 (1999), 715-723
MSC (1991): Primary 42B20
MathSciNet review: 1476118
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Abstract: A generalised integral is used to obtain a Fourier multiplier relation for Calderón-Zygmund operators on $L^1({\mathbb R}^{n})$. In particular we conclude that an operator in our class is injective on $L^1({\mathbb R}^{n})$ if it is injective on $L^2({\mathbb R}^n)$.


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Additional Information

Jonathan Bennett
Affiliation: JCMB, Kings Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland
Email: bennett@maths.ed.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-99-04656-0
Received by editor(s): June 4, 1997
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1999 American Mathematical Society