Geodesic
Local boundary smoothness of an analytic function and its modulus in several dimensions: an announcement
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 30-33 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The drop of the smoothness of an analytic function compared to the smoothness of its modulus is discussed for the unit ball of $\mathbb C^n$. The paper is devoted to local aspects of the problem. 
@article{ZNSL_2018_467_a2,
     author = {I. Vasilyev},
     title = {Local boundary smoothness of an analytic function and its modulus in several dimensions: an announcement},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {30--33},
     year = {2018},
     volume = {467},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a2/}
}
TY  - JOUR
AU  - I. Vasilyev
TI  - Local boundary smoothness of an analytic function and its modulus in several dimensions: an announcement
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2018
SP  - 30
EP  - 33
VL  - 467
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a2/
LA  - en
ID  - ZNSL_2018_467_a2
ER  - 
%0 Journal Article
%A I. Vasilyev
%T Local boundary smoothness of an analytic function and its modulus in several dimensions: an announcement
%J Zapiski Nauchnykh Seminarov POMI
%D 2018
%P 30-33
%V 467
%U http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a2/
%G en
%F ZNSL_2018_467_a2
I. Vasilyev. Local boundary smoothness of an analytic function and its modulus in several dimensions: an announcement. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 30-33. http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a2/

[1] E. Abakumov, O. El-Fallah, K. Kellay, T. Ransford, “Cyclicity in the harmonic Dirichlet space”, Harmonic Analysis, Function Theory, Operator Theory, and Their Applications, Theta Ser. Adv. Math., Theta, Bucharest, 2017, 1–10 | MR

[2] J. E. Brennan, “Approximation in the mean by polynomials on non-Carathéodory domains”, Ark. Mat., 15:1–2 (1977), 117–168 | DOI | MR | Zbl

[3] J. Mashreghi, M. Shabankhah, “Zero sets and uniqueness sets with one cluster point for the Dirichlet space”, J. Math. Analys. Applic., 357:2 (2009), 498–503 | DOI | MR | Zbl

[4] B. A. Taylor, D. L. Williams, “Zeros of Lipschitz functions analytic in the unit disc”, Michigan Math. J., 18:2 (1971), 129–139 | DOI | MR | Zbl

[5] J. Bruna, J. Ortega, “Closed finitely generated ideals in algebras of holomorphic functions and smooth to the boundary in strictly pseudoconvex domains”, Math. Annalen, 268 (1984), 137–158 | DOI | MR

[6] A. V. Vasin, S. V. Kislyakov, A. N. Medvedev, “Local smoothness of an analytic function compared to the smoothness of its modules”, Algebra Analiz, 25:3 (2013), 52–85 | MR | Zbl

[7] V. P. Havin, F. A. Shamoyan, “Analytic functions with the boundary values having Lipschitz module”, Zap. Nauchn. Semin. LOMI, 19, 1970, 237–239 | MR | Zbl

[8] N. A. Shirokov, “Smoothness of a holomorphic function in a ball and smoothness of its modulus on the sphere”, Zap. Nauchn. Semin. POMI, 447, 2016, 123–128 | MR

[9] N. A. Shirokov, Analytic functions smooth up to the boundary, Springer Verlag, 1988 | MR | Zbl

[10] W. Rudin, Function theory in the unit ball of $\mathbb C^n$, Springer-Verlag, New York, 1980 | MR

[11] R. A. DeVore, R. C. Sharpley, Maximal functions measuring smoothness, Mem. Amer. Math. Soc., 47, no. 293, 1984 | MR