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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1992, Volume 52, Issue 3, Pages 96–101 (Mi mz4704)

Equivalent criterion of Haar and Franklin systems in symmetric spaces

I. Ya. Novikov

Research Institute for Mathematics State University of Voronezh

Abstract: In the present article it is proved that if the Haar and Franklin systems are equivalent in a separable symmetric space $E$, the following condition holds:
$$0<\alpha_E\leqslant\beta_E<1,$$
where $\alpha_E$ and $\beta_E$ are the Boyd indices of the space $E$. It is already known that if condition (1) is fulfilled, it follows that the Haar and Franklin systems are equivalent in the space $E$. Thereby, this estabishes that condition (1) is necessary and sufficient for the equivalence of the Haar and Franklin systems in $E$.
In proving the assertion a number of interesting constructions involving Haar and Franklin polynomials are presented and upper and lower bounds on the Franklin functions applied.

Full text: PDF file (700 kB)

English version:
Mathematical Notes, 1992, 52:3, 943–947

Bibliographic databases:

UDC: 517.5

Citation: I. Ya. Novikov, “Equivalent criterion of Haar and Franklin systems in symmetric spaces”, Mat. Zametki, 52:3 (1992), 96–101; Math. Notes, 52:3 (1992), 943–947

Citation in format AMSBIB
\Bibitem{Nov92} \by I.~Ya.~Novikov \paper Equivalent criterion of Haar and Franklin systems in symmetric spaces \jour Mat. Zametki \yr 1992 \vol 52 \issue 3 \pages 96--101 \mathnet{http://mi.mathnet.ru/mz4704} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1194132} \zmath{https://zbmath.org/?q=an:0795.42017} \transl \jour Math. Notes \yr 1992 \vol 52 \issue 3 \pages 943--947 \crossref{https://doi.org/10.1007/BF01209614} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992LF91500010}