NECESSARY CONDITIONS FOR INTEGRABILITY OF THE FOURIER TRANSFORM

We prove the necessary conditions for the integrability of the Fourier transform. The result is a generalization, on one hand, of the well known necessary condition for absolutely convergent Fourier series and, on the other hand, of an earlier multidimensional result of Trigub. 2000 Mathematics Subject Classiflcation: Primary 42B10; Secondary 42B05.