Generalized Bessel and Riesz potentials on metric measure spaces. (English) Zbl 1166.47056
The authors investigate many interesting properties of generalized Bessel and Riesz operators on metric measure spaces having a contractive strongly continuous semigroup of transformations in \(Lp(\mu)\). Some estimates of the Bessel and Riesz kernels are proved. The authors also study the invertibility of such operators and the relationship between them and subordinate semigoups. Applications to the \(p\)-Laplacian are provided. The Bessel operators are used to define the potential spaces.
Reviewer: Khalil Ezzinbi (Marrakech)
MSC:
| 47H50 | Potential operators (MSC2000) |
| 28A80 | Fractals |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
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