Extended Hardy-littlewood Inequalities and Some Applications
نویسنده
چکیده
We establish conditions under which the extended Hardy-Littlewood inequality ∫ RN H ( |x|, u1(x), . . . , um(x) ) dx ≤ ∫ RN H ( |x|, u1(x), . . . , um(x) ) dx, where each ui is non-negative and u ∗ i denotes its Schwarz symmetrization, holds. We also determine appropriate monotonicity assumptions on H such that equality occurs in the above inequality if and only if each ui 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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