Abstract:

In the paper, the author generalized the Hardy and Littlewood’s theorem to
Ba space, i.e. for all Pm satisfying 1 <  = inf pm ≤  ≤ sup pm < ∞,m = 1, 2, · · · , and
− 1
pm
< s < 1 − 1
pm
, the following inequality
k|x|sHfkBa ≤ A,,sk|x|sfkBa
holds if and only if −1
< s < 1 − 1
.

Key words: Hilbert transformation, Ba space