dc.contributor.author
Kolomoitsev, Y.
dc.contributor.author
Tikhonov, Sergey
dc.date.accessioned
2026-01-21T14:47:31Z
dc.date.available
2026-01-21T14:47:31Z
dc.date.issued
2026-04-01
dc.identifier.uri
http://hdl.handle.net/2072/489174
dc.description.abstract
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.
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dc.description.sponsorship
This research was supported by AP 23488596 and through the program Oberwolfach Research Fellows by the Mathematisches Forschungsinstitut Oberwolfach in 2023. The authors would also like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Discretization and recovery in high-dimensional spaces, where work on this paper was undertaken. This work was supported by EPSRC grant EP/R014604/1. We would also like to thank Hans Feichtinger and Karlheinz Groechenig for their helpful comments on our work.
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dc.format.extent
41 p.
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dc.relation.ispartof
Journal of Complexity
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dc.rights
Attribution 4.0 International
*
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
*
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Marcinkiewicz-Zygmund inequality
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dc.subject.other
Quasi-Banach spaces
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dc.subject.other
Bernstein inequality
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dc.title
Marcinkiewicz–Zygmund inequalities in quasi-Banach function spaces
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dc.type
info:eu-repo/semantics/article
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dc.description.version
info:eu-repo/semantics/publishedVersion
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dc.identifier.doi
10.1016/j.jco.2025.101999
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dc.rights.accessLevel
info:eu-repo/semantics/openAccess
