A note on a heat potential and the parabolic variation
A note on the parabolic variation
A condition for solvability of an integral equation which is connected with the first boundary value problem for the heat equation is investigated. It is shown that if this condition is fulfilled then the boundary considered is -Holder. Further, some simple concrete examples are examined.
A numerical solution of the Dirichlet problem on some special doubly connected regions
The aim of this paper is to give a convergence proof of a numerical method for the Dirichlet problem on doubly connected plane regions using the method of reflection across the exterior boundary curve (which is analytic) combined with integral equations extended over the interior boundary curve (which may be irregular with infinitely many angular points).
BMO estimates for biharmonic multiple layer potentials
Boundaries and the Fatou theorem for subelliptic second order operators on solvable Lie groups
Boundary Behavior of Subharmonic Functions on the Unit Disk
Boundary limits of Green's potentials along curves
Boundary properties of second-order partial derivatives of the Poisson integral for a half-space .
Brownian Excursions and Minimal Thinness. Part III: Applications to the Angular Derivative Problem.
Correction of some misprints in my paper “Potentials and boundary value problems” published in “Wissenschaftliche Schriftenreihe der T. H. Karl-Marx-Stadt”
Dirchlet's problem on Green lines and some convergence theorems for Denjoy's domains.
Distribution function inequalities for the density of the area integral
We prove good- inequalities for the area integral, the nontangential maximal function, and the maximal density of the area integral. This answers a question raised by R. F. Gundy. We also prove a Kesten type law of the iterated logarithm for harmonic functions. Our Theorems 1 and 2 are for Lipschitz domains. However, all our results are new even in the case of .
Exakte Größenordnung für das Randverhalten des Poissonschen Integrals von BMO-Funktionen und VMO-Funktionen
Existence of the boundary value of a polyharmonic function.
Fatou and Littlewood related theorems and a convergence property in the R.S. Martin topology.
Internal and external one-sided homogeneous boundary value problems of conjugation for bicircular domains of the space .
Invariant subspaces on open Riemann surfaces. II
We considerably improve our earlier results [Ann. Inst. Fourier, 24-4 (1974] concerning Cauchy-Read’s theorems, convergence of Green lines, and the structure of invariant subspaces for a class of hyperbolic Riemann surfaces.
Local admissible convergence of harmonic functions on non-homogeneous trees
We prove admissible convergence to the boundary of functions that are harmonic on a subset of a non-homogeneous tree equipped with a transition operator that satisfies uniform bounds suitable for transience. The approach is based on a discrete Green formula, suitable estimates for the Green and Poisson kernel and an analogue of the Lusin area function.
Multiplicative square functions.
We study regularity properties of a positive measure in the euclidean space in terms of two square functions which are the multiplicative analogues of the usual martingale square function and of the Lusin area function of a harmonic function. The size of ...
Non-tangential limits of the logarithmic potential