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Weighted estimates for Bochner–Riesz operators on Lorentz spaces

Part of: Harmonic analysis in several variables Linear function spaces and their duals

Published online by Cambridge University Press:  28 February 2022

Sergi Baena-Miret Open the ORCID record for Sergi Baena-Miret [Opens in a new window]  and
María J. Carro Open the ORCID record for María J. Carro [Opens in a new window]
Sergi Baena-Miret
Affiliation:
Departament de Matemàtiques i Informàtica, Universitat de Barcelona, 08007 Barcelona, Spain (sergibaena@ub.edu)
María J. Carro
Affiliation:
Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, Madrid, Spain (mjcarro@ucm.es)
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Abstract

We present new estimates in the setting of weighted Lorentz spaces of operators satisfying a limited Rubio de Francia condition; namely $T$ is bounded on $L^{p}(v)$ for every $v$ in an strictly smaller class of weights than the Muckenhoupt class $A_p$. Important examples will be the Bochner–Riesz operators $BR_\lambda$ with $0<\lambda <{(n-1)}/2$, sparse operators, Hörmander multipliers with a limited regularity condition and rough operators with $\Omega \in L^{r}(\Sigma )$, $1 < r < \infty$.

Keywords

Bochner–Riesz operatorsweighted classical Lorentz spacesMuckenhoupt weightsrestricted weak type extrapolationHörmander multipliersrough operators

MSC classification

Primary: 42B99: None of the above, but in this section
Secondary: 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 2 , April 2023 , pp. 654 - 678
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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