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

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

2009-01-27

arxiv.org/abs/0901.4197v1

Mathematics

Classical Analysis and ODEs

17 pages, accepted for publication

Scientific paper

We give weighted norm inequalities for the maximal fractional operator $ \mathcal M_{q,\beta}$ 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 super spaces 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.

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