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- Aleman, Alexandru, et al.
(författare)
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Estimates in Möbius invariant spaces of analytic functions.
- 2004
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Ingår i: Complex Variables, Theory & Application. - 1563-5066. ; 49:7-9, s. 487-510
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Tidskriftsartikel (refereegranskat)abstract
- We consider a class of spaces of analytic functions on the unit disc which are Möbius invariant and whose topology is essentially determined by a conformal invariant seminorm. Standard examples of such spaces are the Bloch space. BMOA, the Dirichlet spaces and their recent generalizations ${Cal Q}_K$, which make the object of our interest. We prove a general inequality for the seminorms of dilated functions, radial growth estimates, embedding theorems in $L^p$-spaces on the unit disc, as well as integral estimates of exponentials of functions in such spaces. Finally, we discuss some properties of the inner-outer factorization for those ${Cal Q}_K$ spaces which are contained in the Nevanlinna class.
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