Two-parameter Hardy-Littlewood inequalities

Hardy-littlewood Type Inequalities for Laguerre Series

Let {cj} be a null sequence of bounded variation. We give appreciate smoothness and growth conditions on {cj} to obtain the pointwise convergence as well as Lr -convergence of Laguerre series ∑ cj a j . Then, we prove aHardy-Littlewood type inequality ∫∞ 0 |f(t)|r dt≤ C ∑∞ j=0 |cj| j̄1−r/2 for certain r ≤ 1, where f is the limit function of ∑ cj a j . Moreover, we show that if f(x) ∼ ∑cj a j is ...

Extended Hardy-littlewood Inequalities and Some Applications

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....

Note on the Converses of Inequalities of Hardy and Littlewood

The inequalities of Hardy–Littlewood type play very important role in many theorems concerning convergence or summability of orthogonal series. In the applications many times their converses are also very useful. Both the original inequalities and their converses have been generalized in several directions by many authors, among others Leindler (see [5], [6], [7], [8]), Mulholland (see [10]), C...

Hardy-Littlewood-Sobolev inequalities via fast diffusion flows.

We give a simple proof of the λ = d - 2 cases of the sharp Hardy-Littlewood-Sobolev inequality for d≥3, and the sharp Logarithmic Hardy-Littlewood-Sobolev inequality for d = 2 via a monotone flow governed by the fast diffusion equation.

Hardy-Littlewood and Caccioppoli-Type Inequalities for A-Harmonic Tensors