Maximal functions and multiplier theorem for Fourier orthogonal series

2021/12/05 by Xu, Yuan · 1 citation
#41A10 #41A63 #42C10 #42C40 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.02635

Abstract

Under the assumption that orthogonal polynomials of several variables admit an addition formula, we can define a convolution structure and use it to study the Fourier orthogonal expansions on a homogeneous space. We define a maximal function via the convolution structure induced by the addition formula and use it to establish a Marcinkiewicz multiplier theorem. For the homogeneous space defined by a family of weight functions on conic domains, we show that the maximal function is bounded by the Hardy-Littlewood maximal function so that the multiplier theorem holds on conic domains.

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• Approximation and orthogonality on fully symmetric domains

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