Marcinkiewicz–Zygmund inequalities in quasi-Banach function spaces

We obtain Marcinkiewicz-Zygmund (MZ) inequalities in various Banach and quasi-Banach spaces under minimal structural assumptions. 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 unified a...

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Detalles Bibliográficos
Autores: Kolomoitsev, Y., Tikhonov, Sergey
Tipo de recurso: artículo
Fecha de publicación:2026
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/489174
Acceso en línea:http://hdl.handle.net/2072/489174
Access Level:acceso abierto
Palabra clave:Marcinkiewicz-Zygmund inequality
Quasi-Banach spaces
Bernstein inequality
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Descripción
Sumario:We obtain Marcinkiewicz-Zygmund (MZ) inequalities in various Banach and quasi-Banach spaces under minimal structural assumptions. 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 unified approach to deriving MZ inequalities not only for polynomials, but also for other function classes, including entire functions of exponential type, splines, exponential sums, and more. As applications, we derive error estimates for sampling operators, Nikolskii-type inequalities, as well as inequalities for best approximations and moduli of smoothness.