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

Published:2009-12-04
Printed: Jun 2010
• Justin Feuto
• Ibrahim Fofana
• Konin Koua
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## Abstract

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 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.
 Keywords: fractional maximal operator, fractional integral, space of homogeneous type
 MSC Classifications: 42B35 - Function spaces arising in harmonic analysis 42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.) 42B25 - Maximal functions, Littlewood-Paley theory

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