Tangential limits of monotone Sobolev functions.
Temps locaux et l'intégrale d'aire de Lusin
Teoremi di confronto di tipo Harnack per funzioni armoniche in domini con frontiera hölderiana
Teoremi di media e formole di maggiorazione relative alle funzioni biarmoniche
The Absolute Continuity of Elliptic Measure Revisited.
The atomic decomposition of harmonic functions satisfying certain conditions of integrability.
The Besov capacity in metric spaces
We study a capacity theory based on a definition of Hajłasz-Besov functions. We prove several properties of this capacity in the general setting of a metric space equipped with a doubling measure. The main results of the paper are lower bound and upper bound estimates for the capacity in terms of a modified Netrusov-Hausdorff content. Important tools are γ-medians, for which we also prove a new version of a Poincaré type inequality.
The boundary Harnack principle for the fractional Laplacian
We study nonnegative functions which are harmonic on a Lipschitz domain with respect to symmetric stable processes. We prove that if two such functions vanish continuously outside the domain near a part of its boundary, then their ratio is bounded near this part of the boundary.
The boundary-value problems for Laplace equation and domains with nonsmooth boundary
Dirichlet, Neumann and Robin problem for the Laplace equation is investigated on the open set with holes and nonsmooth boundary. The solutions are looked for in the form of a double layer potential and a single layer potential. The measure, the potential of which is a solution of the boundary-value problem, is constructed.
The Brothers Riesz theorem in and Laplace series.
The Cauchy transform of continuous linear functionals and projections on the weighted spaces of analytic functions.
The classification problem for the capacities associated with the Besov and Triebel-Lizorkin spaces
The converse of the Fatou theorem for smooth measures.
The Dirichlet problem for the biharmonic equation in a Lipschitz domain
The Dirichlet problem with non-compact boundary.
The Dynamics of Inner Functions. / Claus I. Doering; Ricardo Mané.
The evolution and Poisson kernels on nilpotent meta-abelian groups
Let S be a semidirect product S = N⋊ A where N is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and A is isomorphic to , k>1. We consider a class of second order left-invariant differential operators on S of the form , where , and for each is left-invariant second order differential operator on N and , where Δ is the usual Laplacian on . Using some probabilistic techniques (e.g., skew-product formulas for diffusions on S and N respectively) we obtain an...
The General Riesz Decomposition and the Specific Order of Excessive Functions.
The Generalized Ahlfors-Heins Theorem in Certain d-Dimensional Cones.
The heat and adjoint heat potentials