Weighted hardy-type inequalities in variable exponent morrey-type spaces

Lukkassen, Dag; Persson, Lars-Erik; Samko, Stefan; Wall, Peter

http://hdl.handle.net/10400.1/12049

Use this identifier to reference this record.

Name:	Description:	Size:	Format:
Weighted Hardy-Type Inequalities in Variable Exponent Morrey-Type Spaces.pdf		1.94 MB	Adobe PDF	Download

Send Feedback

Authors

Abstract(s)

We study the p(.) -> q(.) boundedness of weighted multidimensional Hardy-type operators H-w(alpha(.)) and H-w(alpha(.)) of variable order alpha(x), with radial weight w(vertical bar x vertical bar), from a variable exponent locally generalized Morrey space L-p(.),L-phi(.)(R-n, w) to another L-q(.),L-psi(.)(R-n, w). The exponents are assumed to satisfy the decay condition at the origin and infinity. We construct certain functions, defined by p, alpha, and phi, the belongness of which to the resulting space L-q(.),L-psi(.)(R-n, w) is sufficient for such a boundedness. Under additional assumptions on phi/w, this condition is also necessary. We also give the boundedness conditions in terms of Zygmund-type integral inequalities for the functions phi and phi/w.