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

• Autor(a) principal: Lukkassen, Dag
• Data de Publicação: 2013
• Outros Autores: Persson, Lars-Erik, Samko, Stefan, Wall, Peter
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.1/12049
• topic: Singular integral operators; Potential operators; Lebesgue spaces; Boundedness

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.