Jaak Peetre

A submultiplicative function

Let a≥1 and fa (x)=ln(x+a). It is shown that the function fa is submultiplicative on [0,∞) if and only if a ≥ e. 2. Moreover, the function fa is submultiplicative on [1,∞) if and only if a ≥ ao = 1.7550696584…The techniques the authors describe can also be used for other functions f different from fa.

Hankel operators on planar domains

Let Ω be a bounded domain in the plane whose boundary consists of a finite number of disjoint analytic simple closed curves LetA denote the space of analytic functions on Ω which are square integrable over Ω with respect to area measure and letP denote the orthogonal projection ofL2(Ω,dA) ontoA. A functionb inA induces a Hankel operator (densely defined) onA by the ruleHb(g)=(I−P)bg.This paper continues earlier investigations of the authors and others by determining conditions under whichHb is bounded, compact, or lies in the Schatten-von Neumann idealSp, 1

Comparison of two kinds of Hankel type operators

We compare two kinds of Hankel type operators, the “BJP-operators” introduced by Boman—Janson—Peetre and the “Z-operators” considered by Zhang. We show that every BJP-operator comes as an orthogonal sum ofZ-operators.