Mapping Properties and Composition Structure of Multidimensional Integral Transforms

In this paper mapping properties of multidimensional integral transforms ℑ︁ are considered, which have a composition of the type ℑ︁ f = C ℑ︁ a ℑ︁ f, where C is a constant, ℑ︁ the Fourier transform and a denotes a function of absolute value one. Mapping properties are investigated in the spaces L2(Rn...

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Bibliographic Details
Published in:Mathematische Nachrichten 1991, Vol.152 (1), p.179-190
Main Authors: Glaeske, Hans-Jürgen, Tuan, Vu Kim
Format: Article
Language:English
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Summary:In this paper mapping properties of multidimensional integral transforms ℑ︁ are considered, which have a composition of the type ℑ︁ f = C ℑ︁ a ℑ︁ f, where C is a constant, ℑ︁ the Fourier transform and a denotes a function of absolute value one. Mapping properties are investigated in the spaces L2(Rn) and in Lizorkin spaces of test and generalized functions as well as in Gelfand‐Shilov spaces of test and generalized functions. Two‐ and three‐dimensional examples are discussed.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.19911520116