Riesz transforms for Jacobi expansions
Adam Nowak, Peter Sj\"ogren
TL;DR
This paper introduces and investigates Riesz transforms and conjugate Poisson integrals within the context of multi-dimensional Jacobi expansions, expanding the mathematical understanding of these operators in harmonic analysis.
Contribution
It provides a new framework for defining and analyzing Riesz transforms and conjugate Poisson integrals for Jacobi expansions in multiple dimensions.
Findings
Established boundedness properties of Riesz transforms
Developed new techniques for Jacobi harmonic analysis
Extended classical results to multi-dimensional Jacobi settings
Abstract
We define and study Riesz transforms and conjugate Poisson integrals associated with multi-dimensional Jacobi expansions.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Mathematical functions and polynomials · Algebraic and Geometric Analysis