Generalized fractional integral operators on generalized local Morrey spaces

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Guliyev V., Ismayilova A., Kucukaslan A., ŞERBETÇİ A.

Journal of Function Spaces, vol.2015, 2015 (SCI-Expanded, Scopus)

• Publication Type: Article / Article
• Volume: 2015
• Publication Date: 2015
• Doi Number: 10.1155/2015/594323
• Journal Name: Journal of Function Spaces
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Open Archive Collection: AVESIS Open Access Collection
• Ankara Yıldırım Beyazıt University Affiliated: No

Abstract

© 2015 V. S. Guliyev et al.We study the continuity properties of the generalized fractional integral operator I ρ on the generalized local Morrey spaces L M p, φ ^{x0} and generalized Morrey spaces M p, φ. We find conditions on the triple (φ 1, φ 2, ρ) which ensure the Spanne-type boundedness of I ρ from one generalized local Morrey space L M p, φ 1 ^{x0} to another L M q, φ2 ^{x0}, 1 < p < q < ∞, and from L M1,φ1 ^{x0} to the weak space W L Mq,φ 2 ^{x0}, 1 < q < ∞. We also find conditions on the pair (φ, ρ) which ensure the Adams-type boundedness of I ρ from Mp, φ1/p to Mq,φ1/q for 1 < p < q < ∞ and from M1,φ to W Mq,φ1/q for 1 < q < ∞. In all cases the conditions for the boundedness of I ρ are given in terms of Zygmund-type integral inequalities on (φ 1, φ 2, ρ) and (φ, ρ), which do not assume any assumption on monotonicity of φ1(x, r), φ 2 (x, r), and φ (x, r) in r.