A strong Liouville theorem for -harmonic functions on graphs.
A Tauberian Theorem and Tangential Convergence for Bounded Harmonic Functions on Balls in ...n.
A trace inequality for generalized potentials
A unicity theorem for plurisubharmonic functions
We give sufficient conditions for unicity of plurisubharmonic functions in Cegrell classes.
A Unified Theory of Harmonic Measures and Capacitary Potentials.
A uniform boundary Harnack inequality on non-tangentially accessible domains.
A variational characterization of condenser capacities in within a class of plurisubharmonic functions
Adams inequality on metric measure spaces.
Admissible functions for the Dirichlet space
Zero sets and uniqueness sets of the classical Dirichlet space are not completely characterized yet. We define the concept of admissible functions for the Dirichlet space and then apply them to obtain a new class of zero sets for . Then we discuss the relation between the zero sets of and those of .
Alexander's capacity for intersections of ellipsoids in .
Alexander’s projective capacity for polydisks and ellipsoids in
Alexander’s projective capacity for the polydisk and the ellipsoid in is computed. Sharper versions of two inequalities concerning this capacity and some other capacities in are given. A sequence of orthogonal polynomials with respect to an appropriately defined measure supported on a compact subset K in is proved to have an asymptotic behaviour in similar to that of the Siciak homogeneous extremal function associated with K.
An asymptotic expansion for the discrete harmonic potential.
An energy estimate for the complex Monge-Ampère operator
We prove an energy estimate for the complex Monge-Ampère operator, and a comparison theorem for the corresponding capacity and energy. The results are pluricomplex counterparts to results in classical potential theory.
An example concerning the topological character of the zero-set of a harmonic function.
An extremal plurisubharmonic function associated to a convex pluricomplex Green function with pole at infinity.
An infinite-harmonic analogue of a Lelong theorem and infinite-harmonicity cells.
An integral related to the Cauchy transform on the Sierpiński gasket.
Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and Lp-Liouville properties.
Analytic discs method in complex analysis [Book]
Analytic potential theory over the -adics
Over a non-archimedean local field the absolute value, raised to any positive power , is a negative definite function and generates (the analogue of) the symmetric stable process. For , this process is transient with potential operator given by M. Riesz’ kernel. We develop this potential theory purely analytically and in an explicit manner, obtaining special features afforded by the non-archimedean setting ; e.g. Harnack’s inequality becomes an equality.