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Zapiski Nauchnykh Seminarov POMI, 2004, Volume 315, Pages 121–131 (Mi znsl742)  
This article is cited in 1 scientific paper (total in 1 paper)

On a semigroup of Marcinkiewicz modulars with involution

A. A. Mekler
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Abstract: The set $\mathbf{M}$ of all concave Marcinkiewicz modulars on $[0,1]$ is a semigroup with respect to the usual composition of functions. It is established that some properties of modulars (which are of importance in interpolation and in general Banach space theory) distinguish subsets of $\mathbf{M}$ that form ideals of the semigroup. These ideals turn out to be in a natural duality relation, which is also studied.
Received: 20.11.2004
English version:
Journal of Mathematical Sciences (New York), 2006, Volume 134, Issue 4, Pages 2305–2310
DOI: https://doi.org/10.1007/s10958-006-0106-x
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: A. A. Mekler, “On a semigroup of Marcinkiewicz modulars with involution”, Investigations on linear operators and function theory. Part 32, Zap. Nauchn. Sem. POMI, 315, POMI, St. Petersburg, 2004, 121–131; J. Math. Sci. (N. Y.), 134:4 (2006), 2305–2310
Citation in format AMSBIB
\Bibitem{Mek04}
\by A.~A.~Mekler
\paper On a~semigroup of Marcinkiewicz modulars with involution
\inbook Investigations on linear operators and function theory. Part~32
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 315
\pages 121--131
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl742}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2114019}
\zmath{https://zbmath.org/?q=an:1069.26011}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 134
\issue 4
\pages 2305--2310
\crossref{https://doi.org/10.1007/s10958-006-0106-x}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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