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1

Kelvin transform for (…)-harmonic functions in regular domains

Michalik K., Ryznar M.

Demonstratio Mathematica

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2012

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Vol. 45, nr 2

361-376

EN

We investigate conditional stable processes in a Lipschitz domain D and conditional stable processes in the image of D under the Kelvin transform. We show that, with a suitable change of time, these processes are equal in distribution. As an application, we show the equivalence of the Hardy spaces and the relative Fatou theorem for D and its image.

2

A linear abstract initial value problem with Besov function

Obłoza W.

Czasopismo Techniczne. Nauki Podstawowe

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2010

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R. 107, z. 1-NP

43-55

EN

This article is devoted to the investigation of the abstract linear initial value problem: (*) {[du/du x (t) + A(t)u(t) = f(t)] / [u(s) = x] in a Banach space in a parabolic case with Besov function f. We give sufficient condition for existence and uniqueness of the solution of the problem (*)which may have weak singularity at the origin.

PL

Niniejszy artykuł dotyczy abstrakcyjnego problemu początkowego: (*) {[du/du x (t) + A(t)u(t) = f(t)] / [u(s) = x] w przestrzeni Banacha z funkcją Besova f. Podane są warunki wystarczające na istnienie i jednoznaczność rozwiązania problemu (*) ze słabą osobliwością w punkcie początkowym.

3

Maximal inequalities for U-processes of strongly mixing random variables

Sancetta A.

Probability and Mathematical Statistics

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2009

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Vol. 29, Fasc. 1

155--167

EN

Maximal inequalities for U-processes are required in order to achieve a reduction to the first nonvanishing term in their Hoeffding’s decomposition, which is the relevant quantity for statistical inference. This paper proves new maximal inequalities under strong mixing for U-processes in some function spaces. As an application we derive a uniform central limit theorem.

4

Application of the M RBV S classes to embedding relations of the Besov classes

Szal B.

Demonstratio Mathematica

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2009

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Vol. 42, nr 2

303-322

EN

L. Leindler obtained a necessary and sufficient condition in order to a function is an element of Lp having Fourier coefficients of rest bounded variation belong to the Besov class. In the present paper the analogue of this result is proved with function having Fourier coefficients of mean rest bounded variation. We also discuss embedding relations between the Besov classes.

5

Fractional derivatives of local times of stable Lévy processes as the limits of the occupation time problem in Besov space

Ouhara M. A., Eddahbi M., Ouali M.

Probability and Mathematical Statistics

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2004

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Vol. 24, Fasc. 2

263--279

EN

In this paper, we firstly study the Besov regularity of the local time of symmetric stable processes and of its fractional derivative. Secondly, we establish limit theorems for occupation times of α-symmetric stable processes with 1 < α ≤ 2 in some Besov spaces. Finally, we give the strong approximation version of our limit theorems.