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On the upper bounds for the constants of the Hardy-Littlewood inequality. (English) Zbl 1298.26066
Summary: The best known upper estimates for the constants of the Hardy-Littlewood inequality for $$m$$-linear forms on $$\ell_p$$ spaces are of the form $$(\sqrt{2})^{m - 1}$$. We present better estimates which depend on $$p$$ and $$m$$. An interesting consequence is that if $$p \geq m^2$$ then the constants have a subpolynomial growth as $$m$$ tends to infinity.

##### MSC:
 26D15 Inequalities for sums, series and integrals
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##### References:
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