Abstract
A famous dominated compactness theorem due to Krasnosel'skiǐ states that compactness of a regular linear integral operator in Lp follows from that of a majorant operator. This theorem is extended to the case of the spaces Lp(ċ) (Ω, μ), μ Ω < ∞, with variable exponent p(•), where we also admit power type weights . This extension is obtained as a corollary to a more general similar dominated compactness theorem for arbitrary Banach function spaces for which the dual and associate spaces coincide. The result on compactness in the spaces Lp(ċ)(Ω, μ) is applied to fractional integral operators over bounded open sets.
Original language | English |
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Pages (from-to) | 669-681 |
Number of pages | 13 |
Journal | Complex Analysis and Operator Theory |
Volume | 2 |
Issue number | 4 |
DOIs | |
Publication status | Published - Dec 2008 |
Externally published | Yes |
Keywords
- Banach function space
- Compact majorant
- Compact operators
- Integral operator
- Krasnoselskii theorem
- Potential operator
- Regular operator
- Variable exponent Lebesgue space
ASJC Scopus subject areas
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics