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Boundary behavior of subharmonic functions in nontangential accessible domains

Shiying Zhao (1994)

Studia Mathematica

The following results concerning boundary behavior of subharmonic functions in the unit ball of n are generalized to nontangential accessible domains in the sense of Jerison and Kenig [7]: (i) The classical theorem of Littlewood on the radial limits. (ii) Ziomek’s theorem on the L p -nontangential limits. (iii) The localized version of the above two results and nontangential limits of Green potentials under a certain nontangential condition.

Boundary behaviour of harmonic functions in a half-space and brownian motion

D. L. Burkholder, Richard F. Gundy (1973)

Annales de l'institut Fourier

Let u be harmonic in the half-space R + n + 1 , n 2 . We show that u can have a fine limit at almost every point of the unit cubs in R n = R + n + 1 but fail to have a nontangential limit at any point of the cube. The method is probabilistic and utilizes the equivalence between conditional Brownian motion limits and fine limits at the boundary.In R + 2 it is known that the Hardy classes H p , 0 < p < , may be described in terms of the integrability of the nontangential maximal function, or, alternatively, in terms of the integrability...

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