Riesz potentials, $k,\,p$-capacity, and $p$-modules.

On the (p,q)-Boundedness of Nonisotropic Spherical Riesz Potentials

On duality of modular G-Riesz bases and G-Riesz bases in Hilbert C*-modules

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...

Riesz Transform and Riesz Potentials for Dunkl Transform

Analogous of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weighted functions that are invariant under a reflection group. The L boundedness of these operators is established in certain cases.

Quasiadditivity of Riesz Capacity

holds with some positive constant N . We refer to this inequality as “quasiadditivity”. Quasiadditivity for decompositions into spherical shells has been considered by Landkof [9, Lemma 5.5 in p.304] and Adams [1, Theorem 7.5]. In the case of Green energy (for the definition see Section 5), quasiadditivity for the Whitney decomposition (cf. [14, p.16]) of a half space is discussed in Essén [5]....

Riesz Potentials and Liouville Operators on Fractals

An analogue to the theory of Riesz potentials and Liouville operators in R for arbitrary fractal d-sets is developed. Corresponding function spaces agree with traces of euclidean Besov spaces on fractals. By means of associated quadratic forms we construct strongly continuous semigroups with Liouville operators as infinitesimal generator. The case of Dirichlet forms is discussed separately. As ...