Multi-parameter estimates via operator-valued shifts

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http://hdl.handle.net/10138/307046

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Hytönen , T , Martikainen , H & Vuorinen , E 2019 , ' Multi-parameter estimates via operator-valued shifts ' , Proceedings of the London Mathematical Society , vol. 119 , no. 6 , pp. 1560-1597 . https://doi.org/10.1112/plms.12279

Title: Multi-parameter estimates via operator-valued shifts
Author: Hytönen, Tuomas; Martikainen, Henri; Vuorinen, Emil
Contributor: University of Helsinki, Tuomas Hytönen / Principal Investigator
University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2019-12
Language: eng
Number of pages: 38
Belongs to series: Proceedings of the London Mathematical Society
ISSN: 0024-6115
URI: http://hdl.handle.net/10138/307046
Abstract: We prove the mixed-norm LpLq-boundedness of a general class of singular integral operators having a multi-parameter singularity and acting on vector-valued (UMD Banach lattice-valued) functions. Moreover, families of such operators with uniform assumptions are shown to be not only uniformly bounded but R-bounded, a genuinely stronger property that is often needed in applications. Previous results of this nature only dealt with convolution-type or slightly more general paraproduct-free singular integrals. In contrast, our analysis specifically targets the array of different partial paraproducts that arise in the multi-parameter setting by interpreting them as paraproduct-valued one-parameter operators. This new point-of-view provides a conceptual simplification over the existing representation results for multi-parameter operators, which is a key to the proof of the boundedness of these operators.
Subject: 111 Mathematics
42B20 (primary)
SINGULAR-INTEGRALS
DYADIC SHIFTS
CALDERON
REPRESENTATION
INEQUALITIES
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