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1. Weighted Boundedness of Sublinear Operators in Morrey Spaces. | |||
Hou Weijie,Liu Mingju | |||
Mathematics 04 December 2008 | |||
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Abstract:The classical Morrey spaces were introduced by Morrey to study the local behaviour of solutions to second order elliptic partial differential equations. Since then these spaces play a very import role in studying the regularity of solutions to second order elliptic partial differential equations.As Morrey spaces may be considered as an extension of Lebesgue spaces, it is natural and important to study the weighted boundedness for operaters in Morrey spaces. Much work in this direction has been done.The studying of sublinear operators is very active these years, in this paper, the authors introduce a type of topological structure in the Cartesian product and a set function, and in advance discuss weighted boundedness of sublinear operators in Morrey spaces. The result improve and extend the known results. | |||
TO cite this article:Hou Weijie,Liu Mingju. Weighted Boundedness of Sublinear Operators in Morrey Spaces.[OL].[ 4 December 2008] http://en.paper.edu.cn/en_releasepaper/content/26315 |
2. Boundeness of Generalized Maximal Operaters on Homogeneous Spaces | |||
Weijie Hou , Liu Mingju | |||
Mathematics 25 November 2008 | |||
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Abstract: Maximal functions play a very important role in harmonic analysis. The classical Morrey spaces were introduced by Morrey to study the local behaviour of solutions to second order elliptic partial differential equations. Since then, these spaces play an important role in studying the regularity of solutions to partial differential equations. As homogeneous spaces may be considered as an extension of R^n spaces, it is natural and important to study the boundeness for operaters in Morrey spaces on homogeneous spaces. In this paper, the authors introduce a type of topological structure in the Cartesian product and a set function mapping the balls on homogeneous spaces into the sets in the Cartesian product , and obtain boundeness of generalized operators in Morrey spaces 。Some results have been obtained and the result in this paper improve and extend the known results. | |||
TO cite this article:Weijie Hou , Liu Mingju . Boundeness of Generalized Maximal Operaters on Homogeneous Spaces[OL].[25 November 2008] http://en.paper.edu.cn/en_releasepaper/content/26015 |
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