Weighted norms inequalities for a maximal operator in some subspace of amalgams

Feuto, Justin; Fofana, Ibrahim; Koua, Konin

Weighted norms inequalities for a maximal operator in some subspace of amalgams

Authors

Feuto, Justin

Fofana, Ibrahim

Koua, Konin

Description

We give weighted norm inequalities for the maximal fractional operator $ \mathcal M_{q,β}$ of Hardy-Littlewood and the fractional integral $I_γ$. These inequalities are established between $(L^{q},L^{p}) ^α(X,d,μ)$ spaces (which are super spaces of Lebesgue spaces $L^α(X,d,μ)$, and subspaces of amalgams $(L^{q},L^{p})(X,d,μ)$) and in the setting of space of homogeneous type $(X,d,μ)$. The conditions on the weights are stated in terms of Orlicz norm.
17 pages, accepted for publication