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arXiv · 2411.04119

Marcinkiewicz-Zygmund inequalities in quasi-Banach function spaces

Yurii Kolomoitsev·Sergey Tikhonov
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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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Yurii Kolomoitsev, Sergey Tikhonov. 2024-11-06. Marcinkiewicz-Zygmund inequalities in quasi-Banach function spaces. https://arxiv.org/abs/2411.04119

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