Functions satisfying a discrete mean value property.
Fundamental solutions of differential operators on homogeneous manifolds of negative curvature and related Riesz transforms
Generalization of weierstrass canonical integrals
In this paper we prove that a subharmonic function in ℝm of finite λ-type can be represented (within some subharmonic function) as the sum of a generalized Weierstrass canonical integral and a function of finite λ-type which tends to zero uniformly on compacts of ℝm. The known Brelot-Hadamard representation of subharmonic functions in ℝm of finite order can be obtained as a corollary from this result. Moreover, some properties of R-remainders of λ-admissible mass distributions are investigated.
Generalized condensers and conformal properties of riemannian manifolds with at least two ends
Generalized derivatives of an arbitrary order and the boundary properties of differentiated Poisson integrals for the half-space .
Generalized dirichlet problem in nonlinear potential theory.
Generalized Robin problem in potential theory
Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential
We consider a quasilinear elliptic problem whose left-hand side is a Leray-Lions operator of -Laplacian type. If and the right-hand side is a Radon measure with singularity of order at , then any supersolution in has singularity of order at least at . In the proof we exploit a pointwise estimate of -superharmonic solutions, due to Kilpeläinen and Malý, which involves Wolff’s potential of Radon’s measure.
Generators of the Space of Bounded Biharmonic Functions.
Global higher integrability of jacobians on bounded domains
Gradient potential estimates
Pointwise gradient bounds via Riesz potentials like those available for the Poisson equation actually hold for general quasilinear equations.
Greenian Potentials and Concavity.
Growth and asymptotic sets of subharmonic functions (II)
We study the relation between the growth of a subharmonic function in the half space Rn+1+ and the size of its asymptotic set. In particular, we prove that for any n ≥ 1 and 0 < α ≤ n, there exists a subharmonic function u in the Rn+1+ satisfying the growth condition of order α : u(x) ≤ x-αn+1 for 0 < xn+1 < 1, such that the Hausdorff dimension of the asymptotic set ∪λ≠0A(λ) is exactly n-α. Here A(λ) is the set of boundary points at which f tends to λ along some curve. This...
Growth properties of spherical means for monotone BLD functions in the unit ball.
-cones and potential theory
The -cone is an abstract model for the cone of positive superharmonic functions on a harmonic space or for the cone of excessive functions with respect to a resolvent family, having sufficiently many properties in order to develop a good deal of balayage theory and also to construct a dual concept which is also an -cone. There are given an integral representation theorem and a representation theorem as an -cone of functions for which fine topology, thinnes, negligible sets and the sheaf property...
Hardy spaces and the Dirichlet problem on Lipschitz domains.
Our concern in this paper is to describe a class of Hardy spaces Hp(D) for 1 ≤ p < 2 on a Lipschitz domain D ⊂ Rn when n ≥ 3, and a certain smooth counterpart of Hp(D) on Rn-1, by providing an atomic decomposition and a description of their duals.
Hardy spaces for the Laplacian with lower order perturbations
We consider Hardy spaces of functions harmonic on smooth domains in Euclidean spaces of dimension greater than two with respect to the Laplacian perturbed by lower order terms. We deal with the gradient and Schrödinger perturbations under appropriate Kato conditions. In this context we show the usual correspondence between the harmonic Hardy spaces and the spaces (or the space of finite measures if p = 1) on the boundary. To this end we prove the uniform comparability of the respective harmonic...
Harmonic and analytic functions admitting a distribution boundary value
Harmonic and polyharmonic degeneracy.
Harmonic Bergman spaces with small exponents in the unit ball.