Journal of Fourier Analysis and Applications

, Volume 10, Issue 3, pp 315-324

First online:

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

  • M.L. AgranovskyAffiliated withMathematics Department Bar-Ilan University 52900, Ramat-Gan Email author 
  • , E.K. NarayananAffiliated withHarish-Chandra Research Institute, Chhatnag Road, Jhusi Allahabad, 211019 Email author 

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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.