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A Nevanlinna theorem for superharmonic functions on Dirichlet regular Greenian sets

Neil A. Watson (2005)

Mathematica Bohemica

A generalization of Nevanlinna’s First Fundamental Theorem to superharmonic functions on Green balls is proved. This enables us to generalize many other theorems, on the behaviour of mean values of superharmonic functions over Green spheres, on the Hausdorff measures of certain sets, on the Riesz measures of superharmonic functions, and on differences of positive superharmonic functions.

A nonasymptotic theorem for unnormalized Feynman–Kac particle models

F. Cérou, P. Del Moral, A. Guyader (2011)

Annales de l'I.H.P. Probabilités et statistiques

We present a nonasymptotic theorem for interacting particle approximations of unnormalized Feynman–Kac models. We provide an original stochastic analysis-based on Feynman–Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the -relative error of these weighted particle measures grows linearly with respect to the time horizon yielding what seems to be the first...

A note on the density of the parabolic area integral.

Ileana Iribarren (2001)

Collectanea Mathematica

The density of the area integral for parabolic functions is defined in analogy with the case of harmonic functions. We prove its equivalence with the local time of the associated martingale. Using probabilistic methods, we show its equivalence in L p -norm with the parabolic area function for p>1.

A potential theoretic inequality

Maria Alessandra Ragusa, Pietro Zamboni (2001)

Czechoslovak Mathematical Journal

In this paper is proved a weighted inequality for Riesz potential similar to the classical one by D. Adams. Here the gain of integrability is not always algebraic, as in the classical case, but depends on the growth properties of a certain function measuring some local potential of the weight.

Boundedness of the solution of the third problem for the Laplace equation

Dagmar Medková (2005)

Czechoslovak Mathematical Journal

A necessary and sufficient condition for the boundedness of a solution of the third problem for the Laplace equation is given. As an application a similar result is given for the third problem for the Poisson equation on domains with Lipschitz boundary.

Carleson measure and monogenic functions

S. Bernstein, P. Cerejeiras (2007)

Studia Mathematica

We present necessary and sufficient conditions for a measure to be a p-Carleson measure, based on the Poisson and Poisson-Szegő kernels of the n-dimensional unit ball.

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