[Mathkoll] Korrektur MathKoll. am 25.6/Prof. Matkowsky

[Institut für Mathematik]

Mathematisches Kolloquium

EINLADUNG

zu einem

VORTRAG

von

Prof. Janusz Matkowski
(University of Zielona Góra, Institute of Mathematics)

mit dem Thema:

"Some classical inequalities revisited"

Abstract:
For a measure space $(\Omega, \Sigma, \mu)$ denote by $S = S (\Omega,
\Sigma, \mu)$ the linear real space of all $\mu$-integrable simple functions
$? : \Omega ? \R$. If  $\varphi,\Psi : [0, \infty] ? [0, \infty]$ are
arbitrarily fixed bijections such that $\varphi (0) = \Psi (0) = 0$, then
the functional $\Bbbvarphi, \Psi: S ? [0, \infty]$, $\Bbb\varphi, \Psi(x): =
\Psi (\intl \Omega (x) \varphi ? ?x? d\mu)$, is correctly defined. If there
are $A, B \in \Sigma$ such that $0 < \mu (A) < 1< \mu (B) < \infty$, and
$\Bbb\varphi, \Psi(x + y) ? \Bbb\varphi, \Psi(x) + \Bbb\varphi, \Psi(y),
x,y \in S$, then, under some weak regularity conditions of $\?$ and $\?$,
the functional $\Bbb\varphi, \Psi$ must be equal to the $Lp$-norm up to a
multiplicative constant. This is a converse theorem of the classical
Minkowski inequality. A relevant converse of the Hoelder inequality holds
also true. The ideas of proofs and discussion of the assumption will be
presented.

Zeit: Mittwoch, 25. Juni 2003, 16 Uhr c.t.

Ort: Institut fuer Mathematik der Universitaet Wien, Boltzmanngasse 9,
        ESI - Hoersaal

Martin Kralik
Harald Rindler