Recurrence Criteria for Skew Products of Symmetric Markov Processes.
Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space
We consider the reducibility and unitary equivalence of multiplication operators on the Dirichlet space. We first characterize reducibility of a multiplication operator induced by a finite Blaschke product and, as an application, we show that a multiplication operator induced by a Blaschke product with two zeros is reducible only in an obvious case. Also, we prove that a multiplication operator induced by a multiplier ϕ is unitarily equivalent to a weighted shift of multiplicity 2 if and only if...
Regularity of some nonlinear quantities on superharmonic functions in local Herz-type Hardy spaces.
In this paper, the authors introduce a kind of local Hardy spaces in Rn associated with the local Herz spaces. Then the authors investigate the regularity in these local Hardy spaces of some nonlinear quantities on superharmonic functions on R2. The main results of the authors extend the corresponding results of Evans and Müller in a recent paper.
Relaxation for Dirichlet problems involving a Dirichlet form.
Remark on Ugaheri's maximum principle
Remarks on pluripolar hulls
The aim of the paper is to establish some results on pluripolar hulls and to define pluripolar hulls of certain graphs.
Remarks on the biharmonic Martin boundary and the integral representation of biharmonic functions. (Remarques sur la frontière de Martin biharmonique et la représentation intégrale des fonctions biharmoniques.)
Removable sets for Hölder continuous -harmonic functions on metric measure spaces.
Removable singularities for bounded -harmonic functions and quasi(super)harmonic functions.
Renormalization contracts on nested fractals.
Renormalized solutions of elliptic equations with general measure data
Represenation of a p-harmonic function near a critical point in the plane.
Representation formulas for non-symmetric Dirichlet forms.
Representation of functions by logarithmic potential and reducibility of analytic functions of several variables.
The necessary and sufficient condition that a given plurisubharmonic or a subharmonic function admits the representation by the logarithmic potential (up to pluriharmonic or a harmonic term) is obtained in terms of the Radon transform. This representation is applied to the problem of representation of analytic functions by products of primary factors.
Resistance Conditions and Applications
This paper studies analytic aspects of so-called resistance conditions on metric measure spaces with a doubling measure. These conditions are weaker than the usually assumed Poincaré inequality, but however, they are sufficiently strong to imply several useful results in analysis on metric measure spaces. We show that under a perimeter resistance condition, the capacity of order one and the Hausdorff content of codimension one are comparable. Moreover, we have connections to the Sobolev inequality...
Restricted mean value property in axiomatic potential theory
Riesz potentials and amalgams
Let be a metric space, equipped with a Borel measure satisfying suitable compatibility conditions. An amalgam is a space which looks locally like but globally like . We consider the case where the measure of the ball with centre and radius behaves like a polynomial in , and consider the mapping properties between amalgams of kernel operators where the kernel behaves like when and like when . As an application, we describe Hardy–Littlewood–Sobolev type regularity theorems...
Riesz transforms for symmetric diffusion operators on complete Riemannian manifolds.
Riesz-Martin representation for positive super-polyharmonic functions in a Riemannian manifold.
Rigidity of Certain Harmonic Mappings.