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 (Peer-Reviewed Journal) identifier

  • 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, Scopus

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.