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Mat. Zametki, 1968, Volume 3, Issue 2, Pages 145–156 (Mi mz6661)  

Some properties of functions in Orlicz space

D. V. Salekhov

Voronezh Engineering Building Institute

Abstract: For functions in Orlicz space $L^*_M$, we study the behavior of $\int^\tau_0x^*(t) dt$, where $x^*(t)$ is non-increasing and equimeasurable with $|x(t)|$. We establish the existence of unbounded functions in $L^*_M$, that are not limits of bounded functions and for which $\int_0^\tau x^*(t) dt=o(\tau M^{-1}(1/\tau))$. Moreover, we establish a new criterion for an $N$-function to belong to the class $\Delta_2$ and a sufficiency test for a function to belong to Orlicz space.

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English version:
Mathematical Notes, 1968, 3:2, 92–99

Bibliographic databases:

UDC: 517.5
Received: 27.04.1967

Citation: D. V. Salekhov, “Some properties of functions in Orlicz space”, Mat. Zametki, 3:2 (1968), 145–156; Math. Notes, 3:2 (1968), 92–99

Citation in format AMSBIB
\Bibitem{Sal68}
\by D.~V.~Salekhov
\paper Some properties of functions in Orlicz space
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 2
\pages 145--156
\mathnet{http://mi.mathnet.ru/mz6661}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=229018}
\zmath{https://zbmath.org/?q=an:0163.36401}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 2
\pages 92--99
\crossref{https://doi.org/10.1007/BF01094327}


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