Potential Operators on Cones of Nonincreasing Functions
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 th...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/474681 |
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| author | Alexander Meskhi Ghulam Murtaza |
| author_facet | Alexander Meskhi Ghulam Murtaza |
| author_sort | Alexander Meskhi |
| collection | DOAJ |
| description | 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 ∞. |
| format | Article |
| id | doaj-art-72774338e37448f7a65b18dd10660a00 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-72774338e37448f7a65b18dd10660a002025-02-03T01:30:34ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/474681474681Potential Operators on Cones of Nonincreasing FunctionsAlexander Meskhi0Ghulam Murtaza1A. Razmadze Mathematical Institute, Ivane Javakhishvili Tbilisi State University, 2 University Street, 0143 Tbilisi, GeorgiaAbdus Salam School of Mathematical Sciences, GC University, 68-B New Muslim Town, Lahore, PakistanNecessary 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 ∞.http://dx.doi.org/10.1155/2012/474681 |
| spellingShingle | Alexander Meskhi Ghulam Murtaza Potential Operators on Cones of Nonincreasing Functions Journal of Function Spaces and Applications |
| title | Potential Operators on Cones of Nonincreasing Functions |
| title_full | Potential Operators on Cones of Nonincreasing Functions |
| title_fullStr | Potential Operators on Cones of Nonincreasing Functions |
| title_full_unstemmed | Potential Operators on Cones of Nonincreasing Functions |
| title_short | Potential Operators on Cones of Nonincreasing Functions |
| title_sort | potential operators on cones of nonincreasing functions |
| url | http://dx.doi.org/10.1155/2012/474681 |
| work_keys_str_mv | AT alexandermeskhi potentialoperatorsonconesofnonincreasingfunctions AT ghulammurtaza potentialoperatorsonconesofnonincreasingfunctions |