The Horváth's spaces lfk and the Fourier transform.

In this paper, we establish new properties for the Fourier transform over the space of distributions lfk introduced by Horvath. We prove Abelian theorems for the Fourier transform over the space lfk, k 2 Z, k < 0. Continuity properties and some results concerning regular distributions are studied. We also prove that the Fourier transform is an injection from lfk, k 2 Z, k < 0, into O where this space denotes the union of the varies in Z, which have been given by Horvath. The convolution over for certain regular distributions and its relation with the usual convolution product of functions is exhibited. Finally, some illustrative examples are considered. [ABSTRACT FROM AUTHOR]