Approximation on the sphere by Besov analytic functions

Evgueni Doubtsov

Studia Mathematica (1997)

  • Volume: 124, Issue: 2, page 179-192
  • ISSN: 0039-3223

Abstract

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Boundary values of zero-smooth Besov analytic functions in the unit ball of ℂ n are investigated. Bounded Besov functions with prescribed lower semicontinuous modulus are constructed. Correction theorems for continuous Besov functions are proved. An approximation problem on great circles is studied.

How to cite

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Doubtsov, Evgueni. "Approximation on the sphere by Besov analytic functions." Studia Mathematica 124.2 (1997): 179-192. <http://eudml.org/doc/216407>.

@article{Doubtsov1997,
abstract = {Boundary values of zero-smooth Besov analytic functions in the unit ball of $ℂ^n$ are investigated. Bounded Besov functions with prescribed lower semicontinuous modulus are constructed. Correction theorems for continuous Besov functions are proved. An approximation problem on great circles is studied.},
author = {Doubtsov, Evgueni},
journal = {Studia Mathematica},
keywords = { spaces; space; Besov space; holomorphic functions; inner function behavior},
language = {eng},
number = {2},
pages = {179-192},
title = {Approximation on the sphere by Besov analytic functions},
url = {http://eudml.org/doc/216407},
volume = {124},
year = {1997},
}

TY - JOUR
AU - Doubtsov, Evgueni
TI - Approximation on the sphere by Besov analytic functions
JO - Studia Mathematica
PY - 1997
VL - 124
IS - 2
SP - 179
EP - 192
AB - Boundary values of zero-smooth Besov analytic functions in the unit ball of $ℂ^n$ are investigated. Bounded Besov functions with prescribed lower semicontinuous modulus are constructed. Correction theorems for continuous Besov functions are proved. An approximation problem on great circles is studied.
LA - eng
KW - spaces; space; Besov space; holomorphic functions; inner function behavior
UR - http://eudml.org/doc/216407
ER -

References

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  1. [A1] A. B. Aleksandrov, The existence of inner functions in the ball, Mat. Sb. 118 (160) (1982), 147-163 (in Russian); English transl.: Math. USSR-Sb. 46 (1983), 143-159. Zbl0503.32001
  2. [A2] A. B. Aleksandrov, Inner functions on compact spaces, Funktsional. Anal. i Prilozhen. 18 (2) (1984), 1-13 (in Russian); English transl.: Funct. Anal. Appl. 18 (2) (1984), 87-98. 
  3. [A3] A. B. Aleksandrov, Function theory in the ball, in: Itogi Nauki i Tekhniki 8, VINITI, Moscow, 1985, 115-190 (in Russian); English transl.: G. M. Khenkin and A. G. Vitushkin (eds.), Encyclopaedia Math. Sci. 8 (Several Complex Variables II), Springer, Berlin, 1994, 107-178. 
  4. [BB] F. Beatrous and J. Burbea, Sobolev spaces of holomorphic functions in the ball, Dissertationes Math. 276 (1989). 
  5. [Do] E. Doubtsov, Corrected outer functions, Proc. Amer. Math. Soc., to appear. 
  6. [Du1] Y. Dupain, Gradients des fonctions intérieures dans la boule unité de ℂ n , Math. Z. 193 (1986), 85-94. Zbl0583.32013
  7. [Du2] Y. Dupain, Fonctions intérieures dans la boule unité de ℂ n dont les fonctions traces sont aussi intérieures, ibid. 198 (1988), 191-206. 
  8. [KM] B. Korenblum and J. E. McCarthy, The range of Toeplitz operators on the ball, Rev. Mat. Iberoamericana 12 (1996), 47-61. Zbl0941.47024
  9. [N] J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967. 
  10. [R1] W. Rudin, Function Theory in the Unit Ball of ℂ n , Grundlehren Math. Wiss. 241, Springer, Berlin, 1980. 
  11. [R2] W. Rudin, Inner functions in the unit ball of ℂ n , J. Funct. Anal. 50 (1983), 100-126. Zbl0554.32002
  12. [R3] W. Rudin, New Constructions of Functions Holomorphic in the Unit Ball of ℂ n , CBMS Regional Conf. Ser. in Math. 63, Amer. Math. Soc., Providence, R.I., 1986. 
  13. [Ta] M. Tamm, Sur l'image par une fonction holomorphe bornée du bord d'un domaine pseudoconvexe, C. R. Acad. Sci. Paris 294 (1982), 537-540. Zbl0497.32003
  14. [To] B. Tomaszewski, Interpolation by Lipschitz holomorphic functions, Ark. Mat. 23 (1985), 327-338. Zbl0587.32009

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