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

We study the p · → q·boundedness of weighted multidimensional hardy-type operators h w α·and h w α·of variable order α x,with radial weight w x,from a variable exponent locally generalized morrey space l p ·,φ·r n,w to another l q ·,ψ · r n,w. the exponents are assumed to satisfy the decay condition at the origin and infinity. we construct certain functions,defined by p,α,and φ,the belongness of which to the resulting space l q ·,ψ · r n,w is sufficient for such a boundedness. under additional assumptions on φ / w,this condition is also necessary. we also give the boundedness conditions in terms of zygmund-type integral inequalities for the functions φ and φ / w. © 2013 dag lukkassen et al.