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



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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhauser Boston 2004

Authors and Affiliations

  1. 1.Mathematics Department Bar-Ilan University 52900, Ramat-GanIsrael
  2. 2.Harish-Chandra Research Institute, Chhatnag Road, Jhusi Allahabad, 211019India

Personalised recommendations