Daniel Núñez-Alarcón

Remarks on an inequality of Hardy and Littlewood

Abstract An inequality of Hardy and Littlewood for m-homogeneous polynomials on ℓp spaces is valid for p > m. In this note, among other results, we present an optimal version of this inequality for the case p = m and obtain the optimal constant, when restricted to the case of 2-homogeneous polynomials on ℓ2(ℝ2). In an Appendix we justify why, curiously, the optimal exponents of some Hardy-Littlewood type inequalities do not behave smoothly.

New Lower Bounds for the Constants in the Real Polynomial Hardy–Littlewood Inequality

ABSTRACT In this article, we obtain new lower bounds for the constants of the real scalar-valued Hardy–Littlewood inequality form-homogeneous polynomials on spaces when p = 2m and for certain values of m.