A Bernstein-type inequality for rational functions in weighted Bergman spaces

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• 作者：Anton Baranov^a ; ¹ ; ^{anton.d.baranov@gmail.com} ; Rachid Zarouf^b ; ^{rzarouf@cmi.univ-mrs.fr}
• 关键词：primary ; 32A36 ; 26A33 ; secondary ; 26C15 ; 41A10
• 刊名：Bulletin des Sciences Mathematiques
• 出版年：2013
• 出版时间：June, 2013
• 年：2013
• 卷：137
• 期：4
• 页码：541-556
• 全文大小：174 K

文摘

Given and , we consider the set of rational functions of degree at most n with no poles in , where is the unit disc of the complex plane. We give an asymptotically sharp Bernstein-type inequality for functions in in weighted Bergman spaces with ¡°sub-polynomially¡± decreasing weights. We also prove that this result cannot be extended to weighted Bergman spaces with ¡°super-polynomially¡± decreasing weights.