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

Published online by Cambridge University Press:  20 November 2018

Justin Feuto ,
Ibrahim Fofana  and
Konin Koua
Justin Feuto
Affiliation:
UFR de Mathematiques et Informatique, Université de Cocody, Abidjan, République de Côte d’Ivoire e-mail: justfeuto@yahoo.fr e-mail: fofana ib math ab@yahoo.fr e-mail: kroubla@yahoo.fr
Ibrahim Fofana
Affiliation:
UFR de Mathematiques et Informatique, Université de Cocody, Abidjan, République de Côte d’Ivoire e-mail: justfeuto@yahoo.fr e-mail: fofana ib math ab@yahoo.fr e-mail: kroubla@yahoo.fr
Konin Koua
Affiliation:
UFR de Mathematiques et Informatique, Université de Cocody, Abidjan, République de Côte d’Ivoire e-mail: justfeuto@yahoo.fr e-mail: fofana ib math ab@yahoo.fr e-mail: kroubla@yahoo.fr
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Abstract

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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.

Keywords

42B3542B2042B25fractional maximal operatorfractional integralspace of homogeneous type
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 2 , 01 June 2010 , pp. 263 - 277
Copyright
Copyright © Canadian Mathematical Society 2010

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