Journal of Fourier Analysis and Applications

, Volume 10, Issue 3, pp 315–324

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


DOI: 10.1007/s00041-004-0986-4

Cite this article as:
Agranovsky, M. & Narayanan, E. J. Fourier Anal. Appl. (2004) 10: 315. doi:10.1007/s00041-004-0986-4


It is proved that a nonzero function is not in Lp(Rn) 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 Lp-spaces.

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