A 3G-Theorem for Jordan Domains in ℝ²
We prove a new 3G-Theorem for the Laplace Green function G on an arbitrary Jordan domain D in ℝ². This theorem extends the recent one proved on a Dini-smooth Jordan domain.
A Converse of the Riesz Decompostition Theorem for Harmonic Spaces.
A fine limit property of functions superharmonic outside a manifold
A generalised conical density theorem for unrectifiable sets.
A generalization of the Phragmén-Lindelöf principle for elliptic differential equations.
A generalized area integral estimate and applications
A mean value property of harmonic functions on prolate ellipsoids of revolution.
A Nevanlinna theorem for superharmonic functions on Dirichlet regular Greenian sets
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 Note on L... Spaces of Harmonic Functions.
A Phragmén-Lindelöf Type Theorem for a Certain Class of Generalized Subharmonic Functions.
A probalistic solution of the Neumann problem.
-weighted Caccioppoli-type and Poincaré-type inequalities for -harmonic tensors.
-weighted Caccioppoli-type and Poincaré-type inequalities for -harmonic tensors. Erratum.
A remark on gradients of harmonic functions.
In any C1,s domain, there is nonzero harmonic function C1 continuous up to the boundary such that the function and its gradient on the boundary vanish on a set of positive measure.
A remark on gradients of harmonic functions in dimension ≥3
A Schwarz Lemma for harmonic and hyperbolic-harmonic functions in higher dimensions.
A stability theorem for elliptic Harnack inequalities
We prove a stability theorem for the elliptic Harnack inequality: if two weighted graphs are equivalent, then the elliptic Harnack inequality holds for harmonic functions with respect to one of the graphs if and only if it holds for harmonic functions with respect to the other graph. As part of the proof, we give a characterization of the elliptic Harnack inequality.
A uniqueness theorem for invariantly harmonic functions in the unit ball of Cn.
We prove a boundary uniqueness theorem for harmonic functions with respect to Bergman metric in the unit ball of Cn and give an application to a Runge type approximation theorem for such functions.
A Weak-Type Inequality for Orthogonal Submartingales and Subharmonic Functions
Let X be a submartingale starting from 0, and Y be a semimartingale which is orthogonal and strongly differentially subordinate to X. The paper contains the proof of the sharp estimate . As an application, a related weak-type inequality for smooth functions on Euclidean domains is established.
An application of Bergmann-Whittaker operator.