RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Sib. J. Pure and Appl. Math.: Year: Volume: Issue: Page: Find

 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.

Full text: PDF file (337 kB)
References: PDF file   HTML file

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}