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Bulletin of the London Mathematical Society Advance Access originally published online on April 1, 2008
Bulletin of the London Mathematical Society 2008 40(2):199-209; doi:10.1112/blms/bdm114
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© 2008 London Mathematical Society

Division by inner functions in a class of composition operators on Lipschitz spaces

Miroslav Pavlovic

Faculty of Mathematics
University of Belgrade
Studentski trg 16
11001 Belgrade, p.p. 550
Serbia

Received 11 September 2006. Revision received 19 April 2007.

We prove that the class Formula , where H{Lambda}{alpha} and Formula are holomorphic Lipschitz spaces, has the f-property for p≥1, 0<β<1: If Formula where I is an inner function, then Formula Also we characterize inner functions that belong to Formula for p>0, 0<{alpha}≤1 and 0<β≤1. The results are deduced from a new, derivative-free, characterization of Formula that extends some results of Dyakonov [Acta Math. 178 (1997) 143–167.] and the author [Acta Math. 183 (1999) 141–143; J. Math. Anal. Appl., 326 (2007) 1–11].

2000 Mathematics Subject Classification 47B38, 30H05, 30D55, 46E15, 47B07.

Supported by MNZZS Serbia, Project no. ON144010.


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