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\(\mathcal {N}_p\) Spaces in the Unit Ball \(\mathbb {B}\)

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Theory of Np Spaces

Part of the book series: Frontiers in Mathematics ((FM))

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Abstract

The aim of this chapter is to characterize the \(\mathcal {N}_p\)-spaces in the unit ball as well as the behavior of the weighted composition operators acting on these spaces. We study different properties of the weighted composition operators acting on these spaces.

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References

  1. Cowen, C.C., MacCluer, B.D.: Composition Operators on Spaces of Analytic Functions. Studies in Advanced Mathematics. CRC Press, Boca Raton (1995)

    MATH  Google Scholar 

  2. Duren, P., Weir, R.: The pseudohyperbolic metric and Bergman spaces in the ball. Trans. Am. Math. Soc. 359(1), 63–76 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Hu, B., Khoi, L.H.: Weighted-composition operators on \(\mathcal {N}_p\)-spaces in the ball. C. R. Math. Acad. Sci. Paris 351(19–20), 719–723 (2013)

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  4. MacCluer, B.D., Stroethoff, K., Zhao, R.: Schwarz-Pick type estimates. Complex Var. Theory Appl. 48(8), 711–730 (2003)

    MathSciNet  MATH  Google Scholar 

  5. Palmberg, N.: Composition operators acting on \(\mathcal {N}_p\)-spaces. Bull. Belg. Math. Soc. Simon Stevin 14(3), 545–554 (2007)

    Google Scholar 

  6. Rudin, W.: Function Theory in the Unit Ball of \({\mathbf {C}}^{n}\). Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 241. Springer, New York/Berlin (1980)

    Google Scholar 

  7. Shapiro, J.H.: Composition Operators and Classical Function Theory. Universitext: Tracts in Mathematics. Springer, New York (1993)

    Book  MATH  Google Scholar 

  8. Ueki, S.-I.: Weighted composition operators acting between the \(\mathcal {N}_p\)-space and the weighted-type space \(H^\infty _\alpha \). Indag. Math. (N.S.) 23(3), 243–255 (2012)

    Google Scholar 

  9. Zhu, K.: Spaces of Holomorphic Functions in the Unit Ball. Graduate Texts in Mathematics, vol. 226. Springer, New York (2005)

    Google Scholar 

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Authors and Affiliations

  1. Department of General Education, University of Science and Technology of Hanoi, Vietnam Academy of Science and Technology, Hanoi, Vietnam

    Le Hai Khoi

  2. Department of Mathematics and Statistics, Université Laval, Québec, QC, Canada

    Javad Mashreghi

Authors
  1. Le Hai Khoi
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  2. Javad Mashreghi
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Hai Khoi, L., Mashreghi, J. (2023). \(\mathcal {N}_p\) Spaces in the Unit Ball \(\mathbb {B}\). In: Theory of Np Spaces. Frontiers in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-39704-2_7

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