Generalized Bessel and Riesz Potentials on Metric Measure Spaces

Generalized Bessel and Riesz Potentials on Metric Measure Spaces

There is a rich literature on the study of Bessel and Riesz potentials on the Euclidean space R, see for example the books [23, 20, 1, 16] and the references therein. However, little is known on how to extend the Bessel and Riesz potentials to metric measure spaces in a reasonable way. This issue is interesting in that it is closely related with the study of various current topics, such as the ...

On Continuity of Generalized Riesz Potentials

This study establishes the theorem on continuity of generalized Riesz potentials with non-isotropic kernels depending on (β, γ)-distance. Mathematics Subject Classification: 31B10, 42B20, 47B06

On Generalized Probabilistic Metric Spaces

In the present paper we study some generalized probabilistic metric spaces. Relationships with another deterministic and probabilistic metric structures are analyzed. A contraction condition for mappings with values into such a generalized probabilistic metric space is given. Fixed point results are proved.

On Generalized Complete Metric Spaces

A Riesz decomposition theorem on harmonic spaces without positive potentials

In this paper, we give a new definition of the flux of a superharmonic function defined outside a compact set in a Brelot space without positive potentials. We also give a new notion of potential in a BS space (that is, a harmonic space without positive potentials containing the constants) which leads to a Riesz decomposition theorem for the class of superharmonic functions that have a harmonic...