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Marcinkiewicz-Zygmund inequalities in quasi-Banach function spaces (2411.04119v1)
Published 6 Nov 2024 in math.CA, cs.NA, and math.NA
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.