# 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…

## 3 Citations

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L
\mathfrak {L}
be a nonnegative self-adjoint operator on
L
2
(
X
)
L^2(X)
enjoying Gaussian estimates.…

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