Currently displaying 1 – 3 of 3

Showing per page

Order by Relevance | Title | Year of publication

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

D. L. BurkholderRichard 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...

Page 1

Download Results (CSV)