, Volume 10, Issue 3, pp 315-324
Date: 29 Jan 2004

L p -Integrability, Supports of Fourier Transforms and Uniqueness for Convolution Equations

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Abstract

It is proved that a nonzero function is not in L p (R n ) with p \le 2n/d if its Fourier transform is supported by a d-dimensional submanifold. It is shown that the assertion fails for p > 2n/d and d \ge n/2. The result is applied for obtaining uniqueness theorems for convolution equations in L p -spaces.

Communicated by Carlos Berenstein.