Angle of Contact of Lens and Lunar Maps, and Products of Composition and Iterated Differentiation

Ajay K.Sharma1, Sei-Ichiro Ueki2
1SCHOOL OF MATHEMATICS, SHRI MATA VAISHNO DEVI UNIVERSITY, KAKRYAL, KATRA- 182320, J&K, INDIA.
2Facutty OF ENGINEERING, IBARAKI UNIVERSITY, HITACHI 316 – 8511, JAPAN

Abstract

In this paper, we characterize boundedness and compactness of products of composition operators induced by the lens and the lunar maps and iterated differentiation acting between Hardy and weighted Bergman spaces of the unit disk in terms of the angle of contact of these maps with the unit circle.