[Mathkoll] MathKoll. am 25.6./Prof. Matkowski

[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 (?, ?, ?) denote by S = S (?, ?, ?) the linear real
space of all ?-integrable simple functions ? : ? ? ?. If ?,? : [0, ?) ? [0,
?) are arbitrarily fixed bijections such that ?(0) = ? (0) = 0, then the
functional ??,?: S ? [0, ?), ??,?(x): = ? (??(x) ? ? ?x? d?), is correctly
defined. If there are A, B ? ? such that 0 < ? (A) < 1< ? (B) < ?, and
??,?(x + y) ? ??,?(x) + ??,?(y),  x,y ? S, then, under some weak regularity
conditions of ? and ?, the functional ??,? 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 Hölder 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