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The classical Hausdorff-Young and Hardy-Littlewood-Stein inequalities do not hold for p > 2

coefficients. We prove Hardy–Littlewood and Pitt's inequalities for such series. The corresponding results

for real valued functions and r-convex functions respectively. We also obtain generalizations of some Hardy-Littlewood

. These inequalities are stronger than the Hardy-Littlewood-Sobolev type inequalities. More generally, we consider

belong to Lp. This improves the classical Hardy and Bellman results. A counterpart for the Fourier

inequality for the Kantorovich operators and the Hardy–Littlewood maximal operator, which is of interest

present refinements of some Hardy–Littlewood–Pólya type inequalities and give an application

Hp, 0 < p < 1. We prove the estimate C(p) ≤ πep/[p(1 - p)] in the Hardy-Littlewood inequality We also

Hp, 0 < p < 1. We prove the estimate C(p) ≤ πep/[p(1 - p)] in the Hardy-Littlewood inequality We also

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