Wasthenny Cavalcante

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.

Polynomial and multilinear Hardy-Littlewood inequalities: analytical and numerical approaches

We investigate the growth of the polynomial and multilinear Hardy--Littlewood inequalities. Analytical and numerical approaches are performed and, in particular, among other results, we show that a simple application of the best known constants of the Clarkson inequality improves a recent result of Araujo et al. We also obtain the optimal constants of the generalized Hardy--Littlewood inequality in some special cases.

Bohnenblust-Hille inequalities: analytical and computational aspects

The Bohnenblust-Hille polynomial and multilinear inequalities were proved in 1931 and the determination of exact values of their constants is still an open and challenging problem, pursued by various authors. The present paper briefly surveys recent attempts to attack/solve this problem; it also presents new results, like connections with classical results of the linear theory of absolutely summing operators, and new perspectives.