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Weak inequalities for exit times and analytic functions

D. Burkholder — 1979

Banach Center Publications

Distribution function inequalities for the area integral

D. Burkholder; R. Gundy — 1972

Studia Mathematica

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 $R_{+}^{n + 1}$ , $n \geq 2$ . We show that $u$ can have a fine limit at almost every point of the unit cubs in $R^{n} = \partial R_{+}^{n + 1}$ 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 $H^{p}$ , $0 < p < \infty$ , may be described in terms of the integrability of the nontangential maximal function, or, alternatively, in terms of the...

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