Open Access
1998/1999 Extension of Submultiplicativity and Supermultiplicativity of Orlicz Functions
H. Hudzik, L. Maligranda, M. Mastylo, L. E. Persson
Real Anal. Exchange 24(2): 567-578 (1998/1999).


Results concerning extension of submultiplicativity and supermultiplicativity for Orlicz functions are proved. A typical result is the $\text{following}$: If the Orlicz function $\varphi$ is submultiplicative at infinity, then an Orlicz function $\psi$, which is submultiplicative on ${\mathbb R}_+$, equivalent to $\varphi$ at infinity and satisfying $\psi(u)/u \to 0$ as $u \to 0$ exists if and only if the conjugate function $\varphi^*$ satisfies the $\Delta_2$-condition at infinity. Some complementary results and (counter-)examples are also included.


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H. Hudzik. L. Maligranda. M. Mastylo. L. E. Persson. "Extension of Submultiplicativity and Supermultiplicativity of Orlicz Functions." Real Anal. Exchange 24 (2) 567 - 578, 1998/1999.


Published: 1998/1999
First available in Project Euclid: 28 September 2010

zbMATH: 1039.26003
MathSciNet: MR1704733

Primary: 26A09

Keywords: conjugate functions , Convex functions , extensions , Orlicz functions , submultiplicative functions , supermultiplicative functions

Rights: Copyright © 1999 Michigan State University Press

Vol.24 • No. 2 • 1998/1999
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