Approximation on the sphere by Besov analytic functions

Doubtsov, Evgueni

Studia Mathematica, Tome 122 (1997), p. 179-192 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 1997-01-01

Zbl 0883.32004

EUDML-ID : urn:eudml:doc:216407

@article{bwmeta1.element.bwnjournal-article-smv124i2p179bwm,
     author = {Evgueni Doubtsov},
     title = {Approximation on the sphere by Besov analytic functions},
     journal = {Studia Mathematica},
     volume = {122},
     year = {1997},
     pages = {179-192},
     zbl = {0883.32004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv124i2p179bwm}
}

Doubtsov, Evgueni. Approximation on the sphere by Besov analytic functions. Studia Mathematica, Tome 122 (1997) pp. 179-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv124i2p179bwm/

Bibliographie

[00000] [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. | Zbl 0503.32001

[00001] [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.

[00002] [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.

[00003] [BB] F. Beatrous and J. Burbea, Sobolev spaces of holomorphic functions in the ball, Dissertationes Math. 276 (1989).

[00004] [Do] E. Doubtsov, Corrected outer functions, Proc. Amer. Math. Soc., to appear.

[00005] [Du1] Y. Dupain, Gradients des fonctions intérieures dans la boule unité de $ℂ^{n}$ , Math. Z. 193 (1986), 85-94. | Zbl 0583.32013

[00006] [Du2] Y. Dupain, Fonctions intérieures dans la boule unité de $ℂ^{n}$ dont les fonctions traces sont aussi intérieures, ibid. 198 (1988), 191-206.

[00007] [KM] B. Korenblum and J. E. McCarthy, The range of Toeplitz operators on the ball, Rev. Mat. Iberoamericana 12 (1996), 47-61. | Zbl 0941.47024

[00008] [N] J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967.

[00009] [R1] W. Rudin, Function Theory in the Unit Ball of $ℂ^{n}$ , Grundlehren Math. Wiss. 241, Springer, Berlin, 1980.

[00010] [R2] W. Rudin, Inner functions in the unit ball of $ℂ^{n}$ , J. Funct. Anal. 50 (1983), 100-126. | Zbl 0554.32002

[00011] [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.

[00012] [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. | Zbl 0497.32003

[00013] [To] B. Tomaszewski, Interpolation by Lipschitz holomorphic functions, Ark. Mat. 23 (1985), 327-338. | Zbl 0587.32009