Reverse Carleson measures in Hardy spaces

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• 作者：Andreas Hartmann (1)
  Xavier Massaneda (2)
  Artur Nicolau (3)
  Joaquim Ortega-Cerdà (2)
  
• 关键词：Hardy space ; Carleson measure ; Reverse Carleson measure ; Reproducing kernel ; Reproducing kernel thesis ; Model space ; 30H10 ; 30J99
• 刊名：Collectanea Mathematica
• 出版年：2014
• 出版时间：September 2014
• 年：2014
• 卷：65
• 期：3
• 页码：357-365
• 全文大小：140 KB
• 参考文献：1. Aleksandrov, A.B.: Embedding theorems for coinvariant subspaces of the shift operator II. Zap. Naucn. Semin. S.-Peterburg. Otd. Mat. Inst. Steklov. (POMI) 262, 5-8 (1999)
  2. Aleksandrov, A.B.: On the existence of angular boundary values of pseudocontinuable functions. Zap. Nauchn. Semin. S.-Peterburg. Otd. Mat. Inst. Steklov. (POMI), 222(Issled. po Linein. Oper. i Teor. Funktsii. 23):307, 5-7 (1995)
  3. Aleksandrov, A.B.: Invariant subspaces of shift operators. An axiomatic approach (Russian), investigations on linear operators and the theory of functions, XI. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 113, 7-6 (1981)
  4. Blandignères, A., Fricain, E., Gaunard, F., Hartmann, A., Ross, W.T.: Reverse Carleson embeddings for model spaces. J. Lond. Math. Soc. 88(2), 437-64 (2013)
  5. Cima, J.A., Matheson, A.L., Ross, W.T.: The Cauchy transform. Mathematical Surveys and Monographs, vol. 125. American Mathematical Society, Providence, RI, pp. x+272 (2006)
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  7. Garnett, J.B.: Bounded Analytic Functions. Academic Press, San Diego, CA (1981)
  8. Nikolski, N.K.: Operators, functions, and systems: an easy reading. Mathematical Surveys and Monographs, vols. 1, 92. American Mathematical Society, Providence, RI. Hardy, Hankel, and Toeplitz, Translated from the French by Andreas Hartmann ( 2002)
  9. Lefèvre, P., Li, D., Queffélec, H., Rodríguez-Piazza, L.: Some revisited results about composition operators on Hardy spaces. Rev. Mat. Iberoam. 28(1), 57-6 (2012) CrossRef
  10. Poltoratskii, A.G.: Boundary behavior of pseudocontinuable functions. Algebra i Analiz 5(2), pp. 189-10 (1993). Translation in, St. Petersburg Math. J. 5(2), pp. 389-406 (1994)
  11. Rudin, W.: Real and Complex Analysis, 3rd edn, p. xiv+416. McGraw-Hill Book Co., New York (1987)
  
• 作者单位：Andreas Hartmann (1)
  Xavier Massaneda (2)
  Artur Nicolau (3)
  Joaquim Ortega-Cerdà (2)
  
  1. Institut de Mathématiques de Bordeaux, Université de Bordeaux, 351 cours de la Libération, 33405?, Talence, France
  2. Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007?, Barcelona, Spain
  3. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193?, Bellaterra, Spain
  
• ISSN：2038-4815

文摘

We give a necessary and sufficient condition for a measure \(\mu \) in the closed unit disk to be a reverse Carleson measure for Hardy spaces. This extends a previous result of Lefèvre, Li, Queffélec and Rodríguez-Piazza Lefèvre et al. (Rev Mat Iberoam 28(1):57-6, 2012). We also provide a simple example showing that the analogue for the Paley–Wiener space does not hold. As it turns out the analogue never holds in any model space.