Abstract:
We give a short proof of the known Paley–Marcinkiewicz theorem: the Haar system is an unconditional basis in Lp (p>1). The method of proof consists in a simplification for the Haar system of the method applied in R. Gundy's and other authors' papers for similar problems of the general theory of martingales.
Citation:
V. F. Gaposhkin, “The haar system as an unconditional basis in Lp[0,1]”, Mat. Zametki, 15:2 (1974), 191–196; Math. Notes, 15:2 (1974), 108–111
\Bibitem{Gap74}
\by V.~F.~Gaposhkin
\paper The haar system as an unconditional basis in $L_p[0, 1]$
\jour Mat. Zametki
\yr 1974
\vol 15
\issue 2
\pages 191--196
\mathnet{http://mi.mathnet.ru/mzm7335}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=417676}
\zmath{https://zbmath.org/?q=an:0288.42010|0286.41017}
\transl
\jour Math. Notes
\yr 1974
\vol 15
\issue 2
\pages 108--111
\crossref{https://doi.org/10.1007/BF02102388}
Linking options:
https://www.mathnet.ru/eng/mzm7335
https://www.mathnet.ru/eng/mzm/v15/i2/p191
This publication is cited in the following 3 articles:
R. M. Fernández-Pascual, R. Espejo, M. D. Ruiz-Medina, “Moment and Bayesian wavelet regression from spatially correlated functional data”, Stoch Environ Res Risk Assess, 30:2 (2016), 523
Burgess Davis, Renming Song, Selected Works of Donald L. Burkholder, 2011, 324
G. E. Tkebuchava, “On unconditional convergence with respect to systems of products of bases”, Russian Acad. Sci. Sb. Math., 77:1 (1994), 231–244
Citation in format AMSBIB
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