A distributional Hardy transformation

[摘要] The Hardy'sF-transformF(t)=∫0∞Fv(ty)yf(y)dyis extended to distributions. The corresponding inversion formulaf(x)=∫0∞Cv(tx)tF(t)dtis shown to be valid in the weak distributional sense. This is accomplished by transferring the inversion formula onto the testing function space for the generalized functions under consideration and then showing that the limiting process in the resulting formula converges with respect to the topology of the testing function space.

[学科分类] 数学（综合）