کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4628996 | 1340572 | 2013 | 15 صفحه PDF | دانلود رایگان |
We characterize the analytic self-maps ϕ of the unit disk DD in CC that induce continuous composition operators CϕCϕ from the log-Bloch space Blog(D)Blog(D) to μ -Bloch spaces Bμ(D)Bμ(D) in terms of the sequence of quotients of the μ-Bloch semi-norm of the nth power of ϕ and the log-Bloch semi-norm of the n th power FnFn of the identity function on DD, where μ:D→(0,∞)μ:D→(0,∞) is continuous and bounded. We also obtain an expression that is equivalent to the essential norm of CϕCϕ between these spaces, thus characterizing ϕ such that CϕCϕ is compact. After finding a pairwise norm equivalent family of log-Bloch type spaces that are defined on the unit ball BnBn of CnCn and include the log-Bloch space, we obtain an extension of our boundedness/compactness/essential norm results for CϕCϕ acting on BlogBlog to the case when CϕCϕ acts on these more general log-Bloch-type spaces.
Journal: Applied Mathematics and Computation - Volume 219, Issue 12, 15 February 2013, Pages 6692–6706