On a version of Littlewood-Paley function
On Boundary Behaviour of Harmonic Functions in Hölder Domains.
On boundary Harnack principles and poles of extremal harmonic functions.
On Fatou-Type Theorems for Non-Radial Kernels.
On functions with bounded mixed variance
On integrals of harmonic functions over annuli.
On Lipschitz continuity of harmonic quasiregular maps on the unit ball in .
On the Boundary Behaviour of the Perron Generalized Solution.
On the boundary limits of harmonic functions with gradient in
This paper deals with tangential boundary behaviors of harmonic functions with gradient in Lebesgue classes. Our aim is to extend a recent result of Cruzeiro (C.R.A.S., Paris, 294 (1982), 71–74), concerning tangential boundary limits of harmonic functions with gradient in , denoting the upper half space of the -dimensional euclidean space . Our method used here is different from that of Nagel, Rudin and Shapiro (Ann. of Math., 116 (1982), 331–360); in fact, we use the integral representation...
On the boundary values of harmonic functions.
Over the years many methods have been discovered to prove the existence of a solution of the Dirichlet problem for Laplace's equation. A fairly recent collection of proofs is based on representations of the Green's functions in terms of the Bergman kernel function or some equivalent linear operator [3]. Perhaps the most fundamental of these approaches involves the projection of an arbitrary function onto the class of harmonic functions in a Hilbert space whose norm is defined by the Dirichlet integral...
On the existence of weighted boundary limits of harmonic functions
We study the existence of tangential boundary limits for harmonic functions in a Lipschitz domain, which belong to Orlicz-Sobolev classes. The exceptional sets appearing in this discussion are evaluated by use of Bessel-type capacities as well as Hausdorff measures.
On weighed spaces