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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 $ℝ^{n}$ 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 for p harmonic functions in Lipschitz and starlike Lipschitz ring domains

John L. Lewis, Kaj Nyström (2007)

Annales scientifiques de l'École Normale Supérieure

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 integrability...

Boundary properties of first-order partial derivatives of the Poisson integral for the half-space $ℝ_{k + 1}^{+} (k > 1)$ .

Topuria, S. (1997)

Georgian Mathematical Journal

Boundary properties of second-order partial derivatives of the Poisson integral for a half-space $ℝ_{+}^{k + 1}$ $(k > 1)$ .

Topuria, S. (1998)

Georgian Mathematical Journal

Boundary Value Characterizations for Weighted Hardy Spaces of Harmonic Functions.

Huy-Qui Bui (1990)

Forum mathematicum

Displaying 1 – 9 of 9

Boundary behavior of subharmonic functions in nontangential accessible domains

Boundary behaviour for p harmonic functions in Lipschitz and starlike Lipschitz ring domains

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

Boundary behaviour of positive harmonic functions on Lipschitz domains.

Boundary limits of Green's potentials along curves II. Lipschitz domains

Boundary limits of spherical means for BLD and monotone BLD functions in the unit ball.

Boundary properties of first-order partial derivatives of the Poisson integral for the half-space $ℝ_{k + 1}^{+} (k > 1)$ .

Boundary properties of second-order partial derivatives of the Poisson integral for a half-space $ℝ_{+}^{k + 1}$ $(k > 1)$ .

Boundary Value Characterizations for Weighted Hardy Spaces of Harmonic Functions.

Currently displaying 1 – 9 of 9