WEIGHTED HILBERT TRANSFORM AND Ba METRIC

Abstract

In the paper, the author generalized the Hardy and Littlewood's theorem to Ba space, i.e. for all Pm satisfying 1<α=inf pm≤β≤sup pm<∞,m=1,2,⋯, and -1pm<s<1-1pm, the following inequality |||x|sH f||Ba≤Aα,β,s|||x|sf||Ba holds if and only if-1β<s<1-1α.