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