Asymptotic insights for projection, Gordon-Lewis and Sidon constants in Boolean cube function spaces

2023/02/01 by Defant, Andreas, Galicer, Daniel, Mansilla, Martín +2
#43A75 #46B06 #46B07. Secondary: 42A16 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Primary: 06E30

paper · doi:10.48550/arxiv.2302.00233

Abstract

The main aim of this work is to study important local Banach space constants for Boolean cube function spaces. Specifically, we focus on B_S^N, the finite-dimensional Banach space of all real-valued functions defined on the N-dimensional Boolean cube \-1, +1\^N that have Fourier--Walsh expansions supported on a fixed~family S of subsets of \1, …, N\. Our investigation centers on the projection, Sidon and Gordon--Lewis constants of this function space. We combine tools from different areas to derive exact formulas and asymptotic estimates of these parameters for special types of families S depending on the dimension N of the Boolean cube and other complexity characteristics of the support set S. Using local Banach space theory, we establish the intimate relationship among these three important constants.

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