Studies on concave Young-functions

2006/05/07 by Agbeko, N. K.
#26A09 #26A18 #33B30 #37C25 #47H11 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 47H10 #Secondary 26A06

paper · doi:10.48550/arxiv.math/0605180

Abstract

We succeeded to isolate a special class of concave Young-functions enjoying the so-called density-level property. In this class there is a proper subset whose members have each the so-called degree of contraction denoted by c^∗, and map bijectively the interval [ c^∗, ∞) onto itself. We constructed the fixed point of each of these functions. Later we proved that every positive number b is the fixed point of a concave Young-function having b as degree of contraction. We showed that every concave Young-function is square integrable with respect to a specific Lebesgue measure. We also proved that the concave Young-functions possessing the density-level property constitute a dense set in the space of concave Young-functions with respect to the distance induced by the L²-norm.

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