Weighted Norm Inequalities for a Maximal Operator in Some Subspace of Amalgams

[摘要] We give weighted norm inequalities for the maximal fractional operator $ mathcal M_{q,eta }$ of Hardy–Littlewood and the fractional integral $I_{gamma}$. These inequalities are established between $(L^{q},L^{p}) ^{alpha }(X,d,mu )$ spaces (which are superspaces of Lebesgue spaces $L^{alpha}(X,d,mu)$ and subspaces of amalgams $(L^{q},L^{p})(X,d,mu)$) and in the setting of space of homogeneous type $(X,d,mu)$. The conditions on the weights are stated in terms of Orlicz norm.

[学科分类] 数学（综合）

[关键词] fractional maximal operator;fractional integral;space of homogeneous type