标题： 局部常数和巴尔现象对于解析多项式巴拿赫空间 显示英文标题

标题： Local constants and Bohr's phenomenon for Banach spaces of analytic polynomials

摘要： 本文的主要目的是开发方法，以提供关于巴拿赫空间理论中基本常数之间关系的新见解——特别是投影常数、无条件基常数和戈登-刘易斯常数——对于多元解析多项式的巴拿赫空间$\mathcal{P}_J(X_n)$。 此类包括所有其单项式系数在多指标集$J$之外消失的多项式，并且它配备了有限维巴拿赫空间$X_n = (\mathbb{C}^n, \|\cdot\|)$单位球上的上确界范数。 我们建立了一个通用框架，用于证明这些常数渐近最优行为的定量结果，这些结果取决于空间的维数和多项式的次数。 利用所开发的工具，我们推导了广义巴拿赫序列格的波尔半径的渐近估计。 此外，我们将我们的结果应用于有限维洛伦兹序列空间中局部常数和波尔半径的渐近研究，这需要对相关指标集的组合结构进行更精细的分析。 作为结果，我们在广泛的参数范围内获得了最优结果。 显示英文摘要

摘要： The primary aim of this work is to develop methods that provide new insights into the relationships between fundamental constants in Banach space theory--specifically, the projection constant, the unconditional basis constant and the Gordon-Lewis constant--for the Banach space $\mathcal{P}_J(X_n)$ of multivariate analytic polynomials. This class consists of all polynomials whose monomial coefficients vanish outside the set of multi-indices $J$, and it is equipped with the supremum norm on the unit sphere of the finite-dimensional Banach space $X_n = (\mathbb{C}^n, \|\cdot\|)$. We establish a~general framework for proving quantitative results on the asymptotic optimal behavior of these constants, which depend on both the dimension of the space and the degree of the polynomials. Using the tools developed, we derive asymptotic estimates of the Bohr radius for general Banach sequence lattices. Additionally, we apply our results to the asymptotic study of local constants and the Bohr radius within finite-dimensional Lorentz sequence spaces, which requires a~refined analysis of the combinatorial structure of the associated index sets. As a consequence, we obtain optimal results across a broad range of parameters.