A Family of Optimal Conditions for the Absence of Bound States in a Potential
A fine limit property of functions superharmonic outside a manifold
A general continuity principle
A general definition of capacity
One gives a general definition of capacity which includes -capacity, extremal length and a quantity defined by N.G. Meyers.
A generalised conical density theorem for unrectifiable sets.
A Probabilistic Proof and Applications of Wiener's Test for the Heat Operator.
A Theory of Capacities for Potentials of Functions in Lebesgue Classes.
An generalization of the Riesz potential
An integral inequality for capacities.
An inversion formula and a note on the Riesz kernel
For potentials , where and are certain Schwartz distributions, an inversion formula for is derived. Convolutions and Fourier transforms of distributions in -spaces are used. It is shown that the equilibrium distribution with respect to the Riesz kernel of order , , of a compact subset of has the following property: its restriction to the interior of is an absolutely continuous measure with analytic density which is expressed by an explicit formula.
Another extension of Orlicz--Sobolev spaces to metric spaces.
Behavior at infinity of convolution type integrals.
Bessel potentials in Orlicz spaces.
It is shown that Bessel potentials have a representation in term of measure when the underlying space is Orlicz. A comparison between capacities and Lebesgue measure is given and geometric properties of Bessel capacities in this space are studied. Moreover it is shown that if the capacity of a set is null, then the variation of all signed measures of this set is null when these measures are in the dual of an Orlicz-Sobolev space.
Boundary limits of spherical means for BLD and monotone BLD functions in the unit ball.
Boundary Minimum Principles in Potential Theory.
Boundedness of generalized fractional integral operators on Orlicz spaces near over metric measure spaces
We are concerned with the boundedness of generalized fractional integral operators from Orlicz spaces near to Orlicz spaces over metric measure spaces equipped with lower Ahlfors -regular measures, where is a function of the form and is of log-type. We give a generalization of paper by Mizuta et al. (2010), in the Euclidean setting. We deal with both generalized Riesz potentials and generalized logarithmic potentials.
Bounds for capacities in terms of asymmetry.
Capacitary Inequalities of the Brunn-Minkowski Type.
Capacitary type estimates in strongly nonlinear potential theory and applications.
In this article a general result on smooth truncation of Riesz and Bessel potentials in Orlicz-Sobolev spaces is given and a capacitary type estimate is presented. We construct also a space of quasicontinuous functions and an alternative characterization of this space and a description of its dual are established. For the Riesz kernel Rm, we prove that operators of strong type (A, A), are also of capacitaries strong and weak types (m,A).
Capacities associated to the Siciak extremal function