On <IMG BORDER="0" SRC="/proc/2006-134-10/S0002-9939-06-08349-3/gif-title0/img1.gif" >-norms of meromorphic functions with fixed poles期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On -norms of meromorphic functions with fixed poles

Authors:	A D Baranov

Institution:	Department of Mathematics and Mechanics, St. Petersburg State University, 28, Universitetskii pr., St. Petersburg, 198504, Russia

Abstract:	We study boundedness of the differentiation and embedding operators in the shift-coinvariant subspaces ${K_B^1}$ generated by Blaschke products with sparse zeros, that is, in the spaces of meromorphic functions with fixed poles in the lower half-plane endowed with -norm. We answer negatively the question of K.M. Dyakonov about the necessity of the condition $B'\in L^\infty(\mathbb{R})$ for the boundedness of the differentiation on ${K_B^1}$ . Our main tool is a construction of an unconditional basis of rational fractions in ${K_B^1}$ .

Keywords:	Blaschke products shift-coinvariant subspaces Bernstein's inequality unconditional basis

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