Definition and Properties of the Libera Operator on Mixed Norm Spaces
| Autor: | Miroslav Pavlovic |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | The Scientific World Journal, Vol 2014 (2014) |
| Druh dokumentu: | article |
| ISSN: | 2356-6140 1537-744X |
| DOI: | 10.1155/2014/590656 |
| Popis: | We consider the action of the operator ℒg(z)=(1-z)-1∫z1f(ζ)dζ on a class of “mixed norm” spaces of analytic functions on the unit disk, X=Hα,νp,q, defined by the requirement g∈X⇔r↦(1-r)αMp(r,g(ν))∈Lq([0,1],dr/(1-r)), where 1≤p≤∞, 00, and ν is a nonnegative integer. This class contains Besov spaces, weighted Bergman spaces, Dirichlet type spaces, Hardy-Sobolev spaces, and so forth. The expression ℒg need not be defined for g analytic in the unit disk, even for g∈X. A sufficient, but not necessary, condition is that ∑n=0∞|g^(n)|/(n+1) |
| Databáze: | Directory of Open Access Journals |
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