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Acta Mathematica Vietnamica

, Volume 43, Issue 3, pp 433–448 | Cite as

On the Structure of \(\mathcal {N}_{p}\)-Spaces in the Ball

  • Bingyang Hu
  • Le Hai Khoi
  • Trieu Le
Article

Abstract

We study the structure of \(\mathcal N_{p}\)-spaces in the ball. In particular, we show that any such space is Moebius-invariant and for 0 < pn, all \(\mathcal N_{p}\)-spaces are different. Our results will be used in the study of operator theory on \(\mathcal N_{p}\)-spaces.

Keywords

\(\mathcal N_{p}\)-space Multiplier Moebius-invariant Carleson measure Weighted composition operator 

Mathematics Subject Classification (2010)

32A36 47B33 

Notes

Acknowledgements

The second-named author is supported in part by MOE’s AcRF Tier 1 grants M4011166.110 (RG24/13) and M4011724.110 (RG128/16).

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological University (NTU)SingaporeSingapore
  3. 3.Department of Mathematics and StatisticsUniversity of ToledoToledoUSA

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