Abstract:
We show that measurable polynomials of degree d are
integrable to every positive power and all their Lp-norms are
equivalent. We also prove a zero-one law for level sets of measurable polynomials
and for sets of convergence of measurable polynomials of fixed degree
on spaces with convex measures. We obtain an estimate for the L1-norm of continuous polynomials in terms of the L1-norm
of their restriction to any set of positive measure.
Bibliography: 19 titles.
Citation:
L. M. Arutyunyan, E. D. Kosov, “Estimates for integral norms of polynomials on spaces with convex measures”, Sb. Math., 206:8 (2015), 1030–1048
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\by L.~M.~Arutyunyan, E.~D.~Kosov
\paper Estimates for integral norms of polynomials on spaces with convex measures
\jour Sb. Math.
\yr 2015
\vol 206
\issue 8
\pages 1030--1048
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Linking options:
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https://doi.org/10.1070/SM2015v206n08ABEH004488
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This publication is cited in the following 10 articles:
Konstantin A. Afonin, Vladimir I. Bogachev, “Kantorovich type topologies on spaces of measures and convergence of barycenters”, CPAA, 22:2 (2023), 597
V. I. Bogachev, “Distributions of polynomials in many variables and Nikolskii-Besov spaces”, Real Anal. Exch., 44:1 (2019), 49–64
V. I. Bogachev, E. D. Kosov, G. I. Zelenov, “Fractional smoothness of distributions of polynomials and a fractional analog of the Hardy-Landau-Littlewood inequality”, Trans. Amer. Math. Soc., 370:6 (2018), 4401–4432
E. D. Kosov, “Fractional smoothness of images of logarithmically concave measures under polynomials”, J. Math. Anal. Appl., 462:1 (2018), 390–406
L. M. Arutyunyan, E. D. Kosov, “Deviation of polynomials from their expectations and isoperimetry”, Bernoulli, 24:3 (2018), 2043–2063
Egor D. Kosov, “Fractional smoothness of images of logarithmically concave measures under polynomials”, Journal of Mathematical Analysis and Applications, 462:1 (2018), 390
V. I. Bogachev, O. G. Smolyanov, Topological vector spaces and their applications, Springer Monographs in Mathematics, Springer, Cham, 2017, x+456 pp.
Georgii I. Zelenov, “On distances between distributions of polynomials”, Theory Stoch. Process., 22(38):2 (2017), 79–85
V. I. Bogachev, “Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures”, Russian Math. Surveys, 71:4 (2016), 703–749
L. M. Arutyunyan, “Absolute Continuity of Distributions of Polynomials on Spaces with Log-Concave Measures”, Math. Notes, 101:1 (2017), 31–38
Citation in format AMSBIB
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