The n-Dimensional Hilbert Transform of Distributions, Its Inversion and Applications
O. P. Singh, Jagdish Narayan Pandey · Canadian Journal of Mathematics · 1990
Pandey and Chaudhary [13] recently developed the theory of Hilbert transform of Schwartz distribution space (DLp)',p > 1 in one dimension using Parseval's types of relations for one dimensional Hilbert transform [17] and noted that their theory coincides with the corresponding theory for the Hilbert transform developed by Schwartz [16] by using the technique of convolution in one dimension. The corresponding theory for the Hilbert transform in n-dimension is considerably harder and will be successfully accomplished in this paper.