Extended Hardy-Littlewood inequalities and some applications |
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Authors: | Hichem Hajaiej |
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Institution: | Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904-4137 |
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Abstract: | We establish conditions under which the extended Hardy-Little- wood inequality where each is non-negative and denotes its Schwarz symmetrization, holds. We also determine appropriate monotonicity assumptions on such that equality occurs in the above inequality if and only if each is Schwarz symmetric. We end this paper with some applications of our results in the calculus of variations and partial differential equations. |
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