Some boundary fractal properties of the convolution transform of measures by an approximate identity
type: Item
instance of: scholarly article
title: Some boundary fractal properties of the convolution transform of measures by an approximate identity
zbMATH Open document ID: 0941.28008
DOI: 10.1007/BF02650664
author: Zhiying Wen
author: Yiping Zhang
publication date: 1999-11-16T00:00:00Z
review text: The authors relate the boundary behavior of a positive harmonic function to the local behavior of its boundary measure. As a consequence, if the measure is multifractal, so is the boundary behavior of the function. The harmonic function is the Poisson transform of the measure. The authors actually prove that similar relations hold between a measure and some of its integral transforms, called convolution transforms. It is related to the works of \textit{N. A. Watson} [J. Lond. Math. Soc., II. Ser. 21, 336-350 (1980; Zbl 0436.35038) and Ann. Acad. Sci. Fenn., Ser. A I, Math. 19, No.~1, 115-132 (1994; Zbl 0793.31001)].
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 31B25
zbMATH DE Number: 1321986
zbMATH Keywords: convolution transform of a measure
zbMATH Keywords: multifractal boundary property
reviewed by: Ai-Hua Fan
MaRDI profile type: Publication
cites work: Initial Singularities of Gauss-Weierstrass Integrals and their Relations to Laplace Transforms and Hausdorff Measures
cites work: Q4282708
cites work: Singular boundary properties of harmonic functions and fractal analysis
cites work: Sur les dimensions de mesures
cites work: Multifractal decompositions of Moran fractals
cites work: Q3342857
cites work: Q4740120
published in: Acta Mathematica Sinica, English Series
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description: scientific article; zbMATH DE number 1321986