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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.
We show that a recent interpolative new proof of the Bohnenblust--Hille inequality, when suitably handled, recovers its best known constants. This seems to be unexpectedly surprising since the known interpolative approaches only provide constants hav
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 $2$-h
The Bohnenblust-Hille inequality and its variants have found applications in several areas of Mathematics and related fields. The control of the constants for the variant for complex $m$-homogeneous polynomials is of special interest for applications
Using elementary techniques, we prove sharp anisotropic Hardy-Littlewood inequalities for positive multilinear forms. In particular, we recover an inequality proved by F. Bayart in 2018.
In this work we provide the best constants of the multiple Khintchine inequality. This allows us, among other results, to obtain the best constants of the mixed $left( ell_{frac{p}{p-1}},ell_{2}right) $-Littlewood inequality, thus ending completely a work started by Pellegrino in cite{pell}.