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TWO-WEIGHT NORM INEQUALITIES FOR VECTOR-VALUED OPERATORS

Part of: Harmonic analysis in several variables Linear function spaces and their duals Integral, integro-differential, and pseudodifferential operators Special classes of linear operators

Published online by Cambridge University Press:  26 July 2016

Carme Cascante  and
Joaquin M. Ortega
Carme Cascante
Affiliation:
Dept. Matemàtica i Informàtica, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain email cascante@ub.edu
Joaquin M. Ortega
Affiliation:
Dept. Matemàtica i Informàtica, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain email ortega@ub.edu
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Abstract

We study two-weight norm inequalities for a vector-valued operator from a weighted $L^{p}(\unicode[STIX]{x1D70E})$-space to mixed norm $L_{l^{s}}^{q}(\unicode[STIX]{x1D707})$ spaces, $1<p<\infty$, $0<q<p$. We apply these results to the boundedness of Wolff’s potentials.

MSC classification

Primary: 47B38: Operators on function spaces (general)
Secondary: 42B25: Maximal functions, Littlewood-Paley theory 46E40: Spaces of vector- and operator-valued functions 47G40: Potential operators
Type
Research Article
Information
Mathematika , Volume 63 , Issue 1 , 2017 , pp. 72 - 91
Copyright
Copyright © University College London 2016 

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