A MAXIMAL FUNCTION CHARACTERIZATION OF THE CLASS H ' i 1 )

@inproceedings{Gundy2010AMF,
  title={A MAXIMAL FUNCTION CHARACTERIZATION OF THE CLASS H ' i 1 )},
  author={Richard F. Gundy and Martin L. Silverstein},
  year={2010}
}
Let u be harmonic in the upper half-plane and 0 < p < co. Then « = ReF for some analytic function F of the Hardy class Hp if and only if the nontangential maximal function of « is in L". A general integral inequality between the nontangential maximal function of u and that of its conjugate function is established. Hardy and Littlewood have shown [6] ([12,1, p. 278]) that if F(z) is an analytic function in the unit disc \z\ < 1, and 0,(0) is the Stolz domain given by the interior of the smallest… 

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