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Register a new userA closed formula for subexponential constants in the multilinear Bohnenblust--Hille inequality
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Authors
Diana Marcela Serrano-Rodriguez
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For the scalar field $mathbb{K}=mathbb{R}$ or $mathbb{C}$, the multilinear Bohnenblust--Hille inequality asserts that there exists a sequence of positive scalars $(C_{mathbb{K},m})_{m=1}^{infty}$ such that %[(sumlimits_{i_{1},...,i_{m}=1}^{N}|U(e_{i_{^{1}}}%,...,e_{i_{m}})|^{frac{2m}{m+1}})^{frac{m+1}{2m}}leq C_{mathbb{K},m}sup_{z_{1},...,z_{m}inmathbb{D}^{N}}|U(z_{1},...,z_{m})|] for all $m$-linear form $U:mathbb{K}^{N}times...timesmathbb{K}% ^{N}rightarrowmathbb{K}$ and every positive integer $N$, where $(e_{i})_{i=1}^{N}$ denotes the canonical basis of $mathbb{K}^{N}$ and $mathbb{D}^{N}$ represents the open unit polydisk in $mathbb{K}^{N}$. Since its proof in 1931, the estimates for $C_{mathbb{K},m}$ have been improved in various papers. In 2012 it was shown that there exist constants $(C_{mathbb{K},m})_{m=1}^{infty}$ with subexponential growth satisfying the Bohnenblust-Hille inequality. However, these constants were obtained via a complicated recursive formula. In this paper, among other results, we obtain a closed (non-recursive) formula for these constants with subexponential growth.
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