Weighted Hardy-type inequalities in variable exponent Morrey-type spaces

Validerad; 2013; 20131205 (andbra)
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.

Persson, Lars-ErikLuleå tekniska universitet,Matematiska vetenskaper(Swepub:ltu)larserik (author)
Samko, StefanUniversidade do Algarve, FCT, Campus de Gambelas (author)
Wall, PeterLuleå tekniska universitet,Matematiska vetenskaper(Swepub:ltu)wall (author)
Narvik University College and Norut NarvikMatematiska vetenskaper (creator_code:org_t)

In:Journal of Function Spaces and Applications: Hindawi Limited0972-68021758-4965

By the author/editor: Lukkassen, Dag; Persson, Lars-Er ...; Samko, Stefan; Wall, Peter

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Mathematical Ana ...

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