Geodesic
Weighted Norm Inequalities for a Maximal Operator in Some Subspace of Amalgams
Canadian mathematical bulletin, Tome 53 (2010) no. 2, pp. 263-277

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DOI

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 ${{\left( {{L}^{q}},\,{{L}^{p}} \right)}^{\alpha }}\left( X,\,d,\,\mu\right)$ spaces (which are superspaces of Lebesgue spaces ${{L}^{\alpha }}\left( X,\,d,\,\mu\right)$ and subspaces of amalgams $\left( {{L}^{q}},\,{{L}^{p}} \right)\left( X,d,\mu\right)$ ) and in the setting of space of homogeneous type $\left( X,d,\mu\right)$ . The conditions on the weights are stated in terms of Orlicz norm.
DOI : 10.4153/CMB-2010-015-x
Mots-clés : 42B35, 42B20, 42B25, fractional maximal operator, fractional integral, space of homogeneous type 
Feuto, Justin; Fofana, Ibrahim; Koua, Konin. Weighted Norm Inequalities for a Maximal Operator in Some Subspace of Amalgams. Canadian mathematical bulletin, Tome 53 (2010) no. 2, pp. 263-277. doi: 10.4153/CMB-2010-015-x
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     title = {Weighted {Norm} {Inequalities} for a {Maximal} {Operator} in {Some} {Subspace} of {Amalgams}},
     journal = {Canadian mathematical bulletin},
     pages = {263--277},
     year = {2010},
     volume = {53},
     number = {2},
     doi = {10.4153/CMB-2010-015-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-015-x/}
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