Holomorphic Bloch spaces on the unit ball in

A. V. Harutyunyan; Wolfgang Lusky

Commentationes Mathematicae Universitatis Carolinae (2009)

  • Volume: 50, Issue: 4, page 549-562
  • ISSN: 0010-2628

Abstract

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This work is an introduction to anisotropic spaces of holomorphic functions, which have -weight and are generalizations of Bloch spaces on a unit ball. We describe the holomorphic Bloch space in terms of the corresponding space. We establish a description of via the Bloch classes for all .

How to cite

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Harutyunyan, A. V., and Lusky, Wolfgang. "Holomorphic Bloch spaces on the unit ball in $C^n$." Commentationes Mathematicae Universitatis Carolinae 50.4 (2009): 549-562. <http://eudml.org/doc/35129>.

@article{Harutyunyan2009,
abstract = {This work is an introduction to anisotropic spaces of holomorphic functions, which have $\omega $-weight and are generalizations of Bloch spaces on a unit ball. We describe the holomorphic Bloch space in terms of the corresponding $L_\omega ^\infty $ space. We establish a description of $(A^p(\omega ))^*$ via the Bloch classes for all $0<p\le 1$.},
author = {Harutyunyan, A. V., Lusky, Wolfgang},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {weighted Bloch spaces; projection; inverse mapping; dual space; weighted Bloch spaces; projection; inverse mapping; dual space},
language = {eng},
number = {4},
pages = {549-562},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Holomorphic Bloch spaces on the unit ball in $C^n$},
url = {http://eudml.org/doc/35129},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Harutyunyan, A. V.
AU - Lusky, Wolfgang
TI - Holomorphic Bloch spaces on the unit ball in $C^n$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 4
SP - 549
EP - 562
AB - This work is an introduction to anisotropic spaces of holomorphic functions, which have $\omega $-weight and are generalizations of Bloch spaces on a unit ball. We describe the holomorphic Bloch space in terms of the corresponding $L_\omega ^\infty $ space. We establish a description of $(A^p(\omega ))^*$ via the Bloch classes for all $0<p\le 1$.
LA - eng
KW - weighted Bloch spaces; projection; inverse mapping; dual space; weighted Bloch spaces; projection; inverse mapping; dual space
UR - http://eudml.org/doc/35129
ER -

References

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  1. Attele R., 10.1155/S016117129000028X, Internat. J. Math. Math. Sci. 13 (1990), no. 1, 193--198. Zbl0701.30045MR1038664DOI10.1155/S016117129000028X
  2. Anderson J.M., Bloch function: The basic theory, Operators and Function Theory (Lancaster, 1984), Reidel, Dordrecht, 1985, pp. 1--17. MR0810441
  3. Arazy J., Multipliers of Bloch functions, University of Haifa, Mathematics Publication Series 54, 1982. 
  4. Bishop C.J., 10.2140/pjm.1990.142.209, Pacific J. Math. 142 (1990), no. 2, 209--225. Zbl0652.30024MR1042042DOI10.2140/pjm.1990.142.209
  5. Djrbashian A.E., Shamoian F.A., Topics in the theory of spaces, Teubner Texts in Math., 105, Teubner, Leipzig, 1988. Zbl0667.30032MR1021691
  6. Djrbashian M.M., On the representation problem of analytic functions, Soobsh. Inst. Matem. Mekh. Akad. Nauk Armyan. SSR 2 (1948), 3--40. 
  7. Harutyunyan A.V., 10.1155/2007/353959, J. Funct. Spaces Appl. 5 (2007), no. 3, 213--230. MR2352842DOI10.1155/2007/353959
  8. Nowak M., Bloch space on the unit ball of , Ann. Acad. Sci. Fenn. Math. 23 (1998), no. 2, 461--473. MR1642142
  9. Rudin W., Function Theory in the Unit Ball of , Springer, New York, Heidelberg, Berlin, 1980. MR0601594
  10. Seneta E., Functions of Regular Variation, (in Russian), Nauka, Moscow, 1985. 
  11. Yang W., Some characterizations of -Bloch spaces on the unit ball of , Acta Math. Sci. (English Ed.) 17 (1997), no. 4, 471--477. MR1613263
  12. Zhu K., Spaces of Holomorphic Functions in the Unit Ball, Graduate Texts in Mathematics, 226, Springer, New York, 2005. Zbl1067.32005MR2115155
  13. Zhou Z., The essential norms of composition operators between generalized Bloch spaces in the polydisc and their applications, 2005, arXiv: math.Fa/0503723v3. Zbl1131.47021

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