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

2009/01/27 by Feuto, Justin, Fofana, Ibrahim, Koua, Konin
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.0901.4197

Abstract

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.

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