BMO–VMO results for fractional integrals in variable exponent Morrey spaces. (July 2019)

• Record Type: Journal Article
• Authors: Rafeiro, Humberto; Samko, Stefan
• Is Part Of: Nonlinear analysis. Volume 184(2019)
• Page Start: 35
• Page End: 43
• Publication Date: 2019-07
• Subjects: 46E30 -- 26A33 -- 43A85; Fractional integral -- Riesz potential -- BMO -- Variable exponent Morrey spaces; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.01.020
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove the boundedness of the fractional integration operator of variable order α ( x ) in the limiting Sobolev case α ( x ) p ( x ) = n − λ ( x ) from variable exponent Morrey spaces L p ⋅, λ ⋅ Ω into BMO ( Ω ), where Ω is a bounded open set. In the case α ( x ) ≡ const, we also show the boundedness from variable exponent vanishing Morrey spaces V L p ⋅, λ ⋅ Ω into VMO ( Ω ). The results seem to be new even when p and λ are constant.