On a class of sublinear operators in variable exponent Morrey-type spaces. Issue 3 (4th March 2022)

• Record Type: Journal Article
• Authors: Rafeiro, H.; Samko, S.
• Is Part Of: Complex variables and elliptic equations. Volume 67:Issue 3(2022)
• Page Start: 683
• Page End: 700
• Publication Date: 2022-03-04
• Subjects: Sublinear operators -- Morrey-type spaces -- variable exponent; 46E30 -- 42B25; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2021.1924156
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : For a class of sublinear operators, we find conditions on the variable exponent Morrey-type space L p ( ⋅ ), q, ω ( ⋅, ⋅ ) ( R n ) ensuring the boundedness in this space. A priori assumptions on this class are that the operators are bounded in L p ( ⋅ ) ( R n ) and satisfy some size condition. This class includes in particular the maximal operator, singular operators with the standard kernel, and the Hardy operators. We also prove embedding of variable exponent Morrey-type spaces into weighted L p ( ⋅ ) -spaces.