Archiv der Mathematik

, Volume 113, Issue 6, pp 649–660 | Cite as

The optimal symmetric quasi-Banach range of the discrete Hilbert transform

  • K. TulenovEmail author


We identify the symmetric quasi-Banach range of the discrete Calderón operator and Hilbert transform acting on a symmetric quasi-Banach sequence space. As an application, we present an example of the optimal range in the case when the domain of those operators is the weak-\(\ell _{1}\) space of sequences.


Symmetric (quasi-)Banach sequence spaces Discrete Hilbert transform Discrete Calderón operator Optimal symmetric range 

Mathematics Subject Classification

Primary 46E30 47B10 46L51 46L52 44A15 Secondary 47L20 47C15 



I would like to thank Professor F. Sukochev for bringing this problem to my attention and for the support of the one year visit to the School of Mathematics and Statistics, UNSW, and the warm atmosphere at the department, where a preliminary version of the paper was written. I would also like to thank Dr. D. Zanin for his very useful comments and helps which led to many corrections and improvements. I thank the anonymous referee for reading the paper carefully and providing thoughtful comments, which improved the exposition of the paper. This work was partially supported by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Al-Farabi Kazakh National UniversityAlmatyKazakhstan
  2. 2.Institute of Mathematics and Mathematical ModelingAlmatyKazakhstan

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