Marcinkiewicz-Zygmund inequalities in quasi-Banach function spaces

2024/11/06 by Yurii Kolomoitsev, Sergey Tikhonov, Kolomoitsev, Yurii +1 · 3 citations
Mathematics · #41A25 #46E30 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2411.04119

openalex publication_date 2024/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain Marcinkiewicz--ygmund (MZ) inequalities in various Banach and quasi-Banach spaces under minimal assumptions on the structural properties of these spaces. Our main results show that the Bernstein inequality in a general quasi-Banach function lattice X implies Marcinkiewicz-Zygmund type estimates in X. We present a general approach to obtain MZ inequalities not only for polynomials but for other function classes including entire functions of exponential type, splines, exponential sums, etc.

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• Mixed modulus of smoothness and best approximation in Lorentz spaces
• Semi-discrete moduli of smoothness and their applications in one- and two- sided error estimates
• Discretization Theorems for Entire Functions of Exponential Type

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