Möbius invariant Besov spaces on the unit ball of C n

Małgorzata Michalska; Maria Nowak; Paweł Sobolewski

Annales UMCS, Mathematica (2011)

  • Volume: 65, Issue: 2, page 87-97
  • ISSN: 2083-7402

Abstract

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We give new characterizations of the analytic Besov spaces Bp on the unit ball B of Cn in terms of oscillations and integral means over some Euclidian balls contained in B.

How to cite

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Małgorzata Michalska, Maria Nowak, and Paweł Sobolewski. " Möbius invariant Besov spaces on the unit ball of C n ." Annales UMCS, Mathematica 65.2 (2011): 87-97. <http://eudml.org/doc/268079>.

@article{MałgorzataMichalska2011,
abstract = {We give new characterizations of the analytic Besov spaces Bp on the unit ball B of Cn in terms of oscillations and integral means over some Euclidian balls contained in B.},
author = {Małgorzata Michalska, Maria Nowak, Paweł Sobolewski},
journal = {Annales UMCS, Mathematica},
keywords = {Besov spaces; conformal Möbius transformation},
language = {eng},
number = {2},
pages = {87-97},
title = { Möbius invariant Besov spaces on the unit ball of C n },
url = {http://eudml.org/doc/268079},
volume = {65},
year = {2011},
}

TY - JOUR
AU - Małgorzata Michalska
AU - Maria Nowak
AU - Paweł Sobolewski
TI - Möbius invariant Besov spaces on the unit ball of C n
JO - Annales UMCS, Mathematica
PY - 2011
VL - 65
IS - 2
SP - 87
EP - 97
AB - We give new characterizations of the analytic Besov spaces Bp on the unit ball B of Cn in terms of oscillations and integral means over some Euclidian balls contained in B.
LA - eng
KW - Besov spaces; conformal Möbius transformation
UR - http://eudml.org/doc/268079
ER -

References

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  3. Hahn, K. T., Youssfi, E. H., Möbius invariant Besov p-spaces and Hankel operators in the Bergman space on the unit ball of Cn, Complex Variables Theory Appl. 17 (1991), 89-104. Zbl0706.47017
  4. Li, S., Wulan, H., Besov space on the unit ball of Cn, Indian J. Math. 48 (2006), no. 2, 177-186. Zbl1102.32002
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  9. Ouyang, C., Yang, W. and Zhao, R., Möbius invariant Qp spaces associated with the Green's function on the unit ball of Cn, Pacific J. Math. 182 (1998), no. 1, 69-99. 
  10. Pavlović, M., A formula for the Bloch norm of a C1-function on the unit ball of Cn, Czechoslovak Math. J. 58(133) (2008), no. 4, 1039-1043. Zbl1174.32003
  11. Pavlović, M., On the Holland-Walsh characterization of Bloch functions, Proc. Edinb. Math. Soc. 51 (2008), 439-441.[WoS] Zbl1165.30016
  12. Ren, G., Tu, C., Bloch space in the unit ball of Cn, Proc. Amer. Math. Soc. 133 (2004), no. 3, 719-726. Zbl1056.32005
  13. Rudin, W., Function Theory in the Unit Ball of Cn, Springer-Verlag, New York, 1980. Zbl0495.32001
  14. Stroethoff, K., The Bloch space and Besov space of analytic functions, Bull. Austral. Math. Soc. 54 (1996), 211-219. Zbl0865.30051
  15. Ullrich, D., Radial limits of M-subharmonic functions, Trans. Amer. Math. Soc. 292 (1985), no. 2, 501-518. Zbl0609.31003
  16. Zhu, K., Spaces of Holomorphic Functions in the Unit Ball, Springer-Verlag, New York, 2005. Zbl1067.32005

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