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Generalized Riesz potentials of functions in Morrey spaces L (1,ϕ;κ)(G) over non-doubling measure spaces
- Source :
- Forum Mathematicum. 32:339-359
- Publication Year :
- 2019
- Publisher :
- Walter de Gruyter GmbH, 2019.
-
Abstract
- This paper proves the boundedness of the generalized Riesz potentials I ρ , μ , τ f {I_{\rho,\mu,\tau}f} of functions in the Morrey space L ( 1 , φ ; κ ) ( G ) {L^{(1,\varphi;\kappa)}(G)} over a general measure space X, with G a bounded open set in X (or G is X ) {X)} , as an extension of earlier results. The modification parameter τ is introduced for the purpose of including the case where the underlying measure does not satisfy the doubling condition. What is new in the present paper is that ρ depends on x ∈ X {x\in X} . An example in the end of this article convincingly explains why the modification parameter τ must be introduced.
Details
- ISSN :
- 14355337 and 09337741
- Volume :
- 32
- Database :
- OpenAIRE
- Journal :
- Forum Mathematicum
- Accession number :
- edsair.doi...........b8c11d7e1851d52ebdcb1fa1a334428e