Page 1 Next

Displaying 1 – 20 of 141

Showing per page

A general definition of capacity

Makoto Ohtsuka (1975)

Annales de l'institut Fourier

One gives a general definition of capacity which includes p -capacity, extremal length and a quantity defined by N.G. Meyers.

An inversion formula and a note on the Riesz kernel

Andrejs Dunkels (1976)

Annales de l'institut Fourier

For potentials U K T = K * T , where K and T are certain Schwartz distributions, an inversion formula for T is derived. Convolutions and Fourier transforms of distributions in ( D L ' p ) -spaces are used. It is shown that the equilibrium distribution with respect to the Riesz kernel of order α , 0 < α < m , of a compact subset E of R m has the following property: its restriction to the interior of E is an absolutely continuous measure with analytic density which is expressed by an explicit formula.

Bessel potentials in Orlicz spaces.

N. Aïssaoui (1997)

Revista Matemática de la Universidad Complutense de Madrid

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.

Boundedness of generalized fractional integral operators on Orlicz spaces near L 1 over metric measure spaces

Daiki Hashimoto, Takao Ohno, Tetsu Shimomura (2019)

Czechoslovak Mathematical Journal

We are concerned with the boundedness of generalized fractional integral operators I ρ , τ from Orlicz spaces L Φ ( X ) near L 1 ( X ) to Orlicz spaces L Ψ ( X ) over metric measure spaces equipped with lower Ahlfors Q -regular measures, where Φ is a function of the form Φ ( r ) = r ( r ) 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.

Capacitary type estimates in strongly nonlinear potential theory and applications.

Noureddine Aissaoui (2001)

Revista Matemática Complutense

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).

Currently displaying 1 – 20 of 141

Page 1 Next