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arXiv · 1502.02173

Sharp values for the constants in the polynomial Bohnenblust-Hille inequality

P. Jiménez-Rodríguez·G. A. Muñoz-Fernández·M. Murillo-Arcila·J. B. Seoane-Sepúlveda
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Abstract

In this paper we prove that the complex polynomial Bohnenblust-Hille constant for $2$-homogeneous polynomials in ${\mathbb C}^2$ is exactly $\sqrt[4]{\frac{3}{2}}$. We also give the exact value of the real polynomial Bohnenblust-Hille constant for $2$-homogeneous polynomials in ${\mathbb R}^2$. Finally, we provide lower estimates for the real polynomial Bohnenblust-Hille constant for polynomials in ${\mathbb R}^2$ of higher degrees.

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P. Jiménez-Rodríguez, G. A. Muñoz-Fernández, M. Murillo-Arcila, J. B. Seoane-Sepúlveda. 2015-02-07. Sharp values for the constants in the polynomial Bohnenblust-Hille inequality. https://arxiv.org/abs/1502.02173

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