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A note on the parabolic variation

Miroslav Dont (2000)

Mathematica Bohemica

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 1 2 -Holder. Further, some simple concrete examples are examined.

A numerical solution of the Dirichlet problem on some special doubly connected regions

Miroslav Dont, Eva Dontová (1998)

Applications of Mathematics

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).

Distribution function inequalities for the density of the area integral

R. Banuelos, C. N. Moore (1991)

Annales de l'institut Fourier

We prove good- λ 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 R + 2 .

Invariant subspaces on open Riemann surfaces. II

Morisuke Hasumi (1976)

Annales de l'institut Fourier

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

Massimo A. Picardello (2010)

Colloquium Mathematicae

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.

María José González, Artur Nicolau (2004)

Revista Matemática Iberoamericana

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 ...

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