Potential Operators on Cones of Nonincreasing Functions
| Autor: | Alexander Meskhi, Ghulam Murtaza |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Journal of Function Spaces and Applications, Vol 2012 (2012) |
| Druh dokumentu: | article |
| ISSN: | 0972-6802 1758-4965 |
| DOI: | 10.1155/2012/474681 |
| Popis: | Necessary and sufficient conditions on weight pairs guaranteeing the two-weight inequalities for the potential operators (Iαf)(x)=∫0∞(f(t)/|x−t|1−α)dt and (ℐα1,α2f)(x,y)=∫0∞∫0∞(f(t,τ)/|x−t|1−α1|y−τ|1−α2)dtdτ on the cone of nonincreasing functions are derived. In the case of ℐα1,α2, we assume that the right-hand side weight is of product type. The same problem for other mixed-type double potential operators is also studied. Exponents of the Lebesgue spaces are assumed to be between 1 and ∞. |
| Databáze: | Directory of Open Access Journals |
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