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WEIGHTED SUBSPACES OF HARDY SPACES H~(p,γ)(D) AND AREA INTEGRALS

In this paper we study the growth of area integrals Ar(f) of analytic function f in the weighted subspaces of Hardy spaces H p,γ(D).For two cases 0p≤2 and 2≤p∞,we give a necessary condition and a sufficient condition such that f∈H p,γ(D) by area integrals Ar(f) of analytic function f respectively.These results generalize the main theorems of F.Holland and J.B.Twomey and remedy an E.G.Kwon's corollary on H p,γ(D) function.