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ANALYSIS IN THE MULTI-DIMENSIONAL BALL

Part of: Nontrigonometric harmonic analysis Harmonic analysis in several variables Other generalizations

Published online by Cambridge University Press:  31 October 2018

Peter Sjögren  and
Tomasz Z. Szarek
Peter Sjögren
Affiliation:
Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-412 96 Göteborg, Sweden email peters@chalmers.se
Tomasz Z. Szarek
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00–656 Warszawa, Poland Department of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02–097 Warszawa, Poland email szarektomaszz@gmail.com
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Abstract

We study the heat semigroup maximal operator associated with a well-known orthonormal system in the $d$-dimensional ball. The corresponding heat kernel is shown to satisfy Gaussian bounds. As a consequence, we can prove weighted $L^{p}$ estimates, as well as some weighted inequalities in mixed norm spaces, for this maximal operator.

MSC classification

Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 42C05: Orthogonal functions and polynomials, general theory 31C25: Dirichlet spaces
Type
Research Article
Information
Mathematika , Volume 65 , Issue 2 , 2019 , pp. 190 - 212
Copyright
Copyright © University College London 2018 

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Footnotes

The second author was partially supported by the National Science Centre of Poland, project no. 2015/19/D/ST1/01178, and by the Foundation for Polish Science START Scholarship.

References

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