# On the polynomial Hardy–Littlewood inequality

@article{Arajo2014OnTP, title={On the polynomial Hardy–Littlewood inequality}, author={Gustavo Ara{\'u}jo and Pablo Jim{\'e}nez-Rodr{\'i}guez and Gustavo A. Mu{\~n}oz-Fern{\'a}ndez and Daniel N{\'u}{\~n}ez-Alarc{\'o}n and Daniel Pellegrino and Juan B. Seoane-Sep{\'u}lveda and Diana Marcela Serrano-Rodr{\'i}guez}, journal={Archiv der Mathematik}, year={2014}, volume={104}, pages={259-270} }

We investigate the behavior of the constants of the polynomial Hardy–Littlewood inequality.

#### 7 Citations

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

- Mathematics
- 2015

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… Expand

Estimates on the norm of polynomials and applications

- Mathematics
- 2015

In this paper, equivalence constants between various polynomial norms are calculated. As an application, we also obtain sharp values of the Hardy--Littlewood constants for $2$-homogeneous polynomials… Expand

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

- Mathematics
- 2018

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… Expand

Equivalent norms in polynomial spaces and applications

- Mathematics
- 2017

Abstract In this paper, equivalence constants between various polynomial norms are calculated. As an application, we also obtain sharp values of the Hardy–Littlewood constants for 2-homogeneous… Expand

Remarks on the Hardy--Littlewood inequality for $m$-homogeneous polynomials and $m$-linear forms

- Mathematics
- 2015

The Hardy--Littlewood inequality for $m$-homogeneous polynomials on $\ell_{p}$ spaces is valid for $p>m.$ In this note, among other results, we present an optimal version of this inequality for the… Expand

Some classical inequalities, summability of multilinear operators and strange functions

- Mathematics
- 2016

This work is divided into three parts. In the first part, we investigate the behavior of the constants of the Bohnenblust–Hille and Hardy–Littlewood polynomial and multilinear inequalities. In the… Expand

Lower bounds for the complex polynomial Hardy–Littlewood inequality

- Mathematics
- 2015

Abstract The Hardy–Littlewood inequality for complex homogeneous polynomials asserts that given positive integers m ≥ 2 and n ≥ 1 , if P is a complex homogeneous polynomial of degree m on l p n with… Expand

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