Tail spaces estimates on Hamming cube and Bernstein--Markov inequality

2022/07/31 by Alexander Volberg, Volberg, Alexander
Mathematics · #41A17 #41A63 #46B07 #46B09 #46B10 #60E15 #Advanced Banach Space Theory #Analysis of PDEs (math.AP) #Approximation Theory and Sequence Spaces #F.2.2 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical functions and polynomials #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2208.00472

openalex publication_date 2022/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note contains some estimates for tail spaces on Hamming cube. We use analytic paraproduct operator for that purpose. We also show several types of Bernstein--Markov inequalities for Banach space valued functions on Hamming cube. Here the novelty is in getting rid of some irritating logarithms and in proving Bernstein--Markov inequalities for |∇ f|_X rather than for Δ^1/2 f for X valued polynomials on Hamming cube.

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