A note on the Fourier transform of fractal measures
type: Item
instance of: scholarly article
title: A note on the Fourier transform of fractal measures
zbMATH Open document ID: 1083.42006
published in: Mathematical Research Letters
publication date: 2004-12-29T00:00:00Z
review text: The paper is concerned with the decay of the averages of the Fourier transform of measures with finite energy. In the first part of the paper, the author generalizes a result of \textit{P. Sjölin} in [Ann. Acad. Sci. Fenn., Math. 22, No. 1, 227--236 (1997; Zbl 0865.42007)]. The author also extends and gives a different proof to \textit{T. Wolff}'s result [Int. Math. Res. Not. 1999, No. 10, 547--567 (1999); addendum ibid. 88, No. 1, 35--39 (2002; Zbl 0930.42006)] which may be regarded as a weighted version of the Stein-Tomas restriction theorem dealing with estimates for the \(L^q\)-norm of the inverse Fourier transforms of certain \(L^2\) functions. In the second part of the paper, the author considers the case of normalized surface measures on the cones in the 3-dimensional Euclidean space.
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 28A12
Mathematics Subject Classification ID: 28A75
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 37F35
zbMATH DE Number: 2123930
zbMATH Keywords: Fourier transform of a measure
zbMATH Keywords: energy of a measure
zbMATH Keywords: distance set problem
zbMATH Keywords: Stein-Tomas restriction theorem
author: Mehmet Burak Erdoğan
MaRDI profile type: Publication
full work available at URL: mrl.2004.v11.n3.a3
OpenAlex ID: W2170213212
DOI: 10.4310/MRL.2004.V11.N3.A3
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description: scientific article; zbMATH DE number 2123930