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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2006, Volume 6, Issue 2, Pages 33–56 (Mi vngu230)  

The scales of spaces $L_p$ and their connection with Orlicz spaces

A. E. Mamontov


Abstract: We describe the classes of measurable functions which are estimated in the spaces $L_p$ with the norm $\omega(p)$ for all $p\in(\alpha,\beta)$. It is well-known for some simple functions $\omega$ and $\beta=+\infty$ that such classes are embedded into the appropriate Orlicz spaces. In this article we study the connection between these classes and other symmetric (Lorentz, Marcinkiewicz and Orlicz) spaces for arbitrary $\omega$, $\alpha$ and $\beta$. Our main goal is to show two-sided embedding or coincidence with Orlicz spaces.

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Document Type: Article
UDC: 517.982

Citation: A. E. Mamontov, “The scales of spaces $L_p$ and their connection with Orlicz spaces”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 6:2 (2006), 33–56

Citation in format AMSBIB
\Bibitem{Mam06}
\by A.~E.~Mamontov
\paper The scales of spaces $L_p$ and their connection with Orlicz spaces
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2006
\vol 6
\issue 2
\pages 33--56
\mathnet{http://mi.mathnet.ru/vngu230}


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  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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