Boundary Value Characterizations for Weighted Hardy Spaces of Harmonic Functions.
Boundary value problems for harmonic and minimal maps of surfaces into manifolds
Boundary values of harmonic functions in mixed norm spaces and their atomic structure
Boundedness of generalized fractional integral operators on Orlicz spaces near over metric measure spaces
We are concerned with the boundedness of generalized fractional integral operators from Orlicz spaces near to Orlicz spaces over metric measure spaces equipped with lower Ahlfors -regular measures, where is a function of the form and is of log-type. We give a generalization of paper by Mizuta et al. (2010), in the Euclidean setting. We deal with both generalized Riesz potentials and generalized logarithmic potentials.
Boundedness of the solution of the third problem for the Laplace equation
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.
Bounds for capacities in terms of asymmetry.
Brownian Motion and Eigenvalues for the Dirichlet Laplacian.
Brownian motion and generalized analytic and inner functions
Let be a mapping from an open set in into , with . To say that preserves Brownian motion, up to a random change of clock, means that is harmonic and that its tangent linear mapping in proportional to a co-isometry. In the case , , such conditions signify that corresponds to an analytic function of one complex variable. We study, essentially that case , , in which we prove in particular that such a mapping cannot be “inner” if it is not trivial. A similar result for , would solve...
approximations of convex, subharmonic, and plurisubharmonic functions
Capacitary Inequalities of the Brunn-Minkowski Type.
Capacitary type estimates in strongly nonlinear potential theory and applications.
In this article a general result on smooth truncation of Riesz and Bessel potentials in Orlicz-Sobolev spaces is given and a capacitary type estimate is presented. We construct also a space of quasicontinuous functions and an alternative characterization of this space and a description of its dual are established. For the Riesz kernel Rm, we prove that operators of strong type (A, A), are also of capacitaries strong and weak types (m,A).
Capacities associated to the Siciak extremal function
Carleson measure and monogenic functions
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.
Carleson measures for weighted harmonic mixed norm spaces on bounded domains in
We study weighted mixed norm spaces of harmonic functions defined on smoothly bounded domains in . Our principal result is a characterization of Carleson measures for these spaces. First, we obtain an equivalence of norms on these spaces. Then we give a necessary and sufficient condition for the embedding of the weighted harmonic mixed norm space into the corresponding mixed norm space.
Cauchy-Szegö integrals for systems of harmonic functions
Characterization of best harmonic and superharmonic L1-approximations.
Choquetova teorie a Dirichletova úloha
Choquetova teorie kapacit
Classes de Bergman de fonctions harmoniques
Comparisons of kernel functions boundary Harnack principle and relative Fatou theorem on Lipschitz domains
On a Lipschitz domain in , three theorems on harmonic functions are proved. The first (boundary Harnack principle) compares two positive harmonic functions at interior points near an open subset of the boundary where both functions vanish. The second extends some familiar geometric facts about the Poisson kernel on a sphere to the Poisson kernel on . The third theorem, on non-tangential limits of quotient of two positive harmonic functions in , generalizes Doob’s relative Fatou theorem on a...