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On the Fourier transforms

Published online by Cambridge University Press:  17 April 2009

Hwai-chiuan Wang
Hwai-chiuan Wang
Affiliation:
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300, Republic of China.
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Abstract

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In this article we give a new proof of the theorem that a positive even convex function on the real line, which vanishes at infinity, is the Fourier transform of an integrable function. Related results in several variables are also proved. As an application of our results we solve the factorization problem of Sobolev algebras.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 31 , Issue 2 , April 1985 , pp. 171 - 179
Copyright
Copyright © Australian Mathematical Society 1985

References

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