Geodesic
Outer functions in classes of analytic functions of variable smoothness
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 47, Tome 480 (2019), pp. 206-213
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We introduce classes of analytic functions in a disc and holomorphic functions in a ball that satisfy a Hölder condition in a Lebesgue norm with variable exponent. We describe outer functions in the disc and state the drop of the smoothness of a function in comparison with the smoothness of its modulus on the boundary in the case of the disc and the ball. 
@article{ZNSL_2019_480_a14,
     author = {N. A. Shirokov},
     title = {Outer functions in classes of analytic functions of variable smoothness},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {206--213},
     year = {2019},
     volume = {480},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_480_a14/}
}
TY  - JOUR
AU  - N. A. Shirokov
TI  - Outer functions in classes of analytic functions of variable smoothness
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2019
SP  - 206
EP  - 213
VL  - 480
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2019_480_a14/
LA  - ru
ID  - ZNSL_2019_480_a14
ER  - 
%0 Journal Article
%A N. A. Shirokov
%T Outer functions in classes of analytic functions of variable smoothness
%J Zapiski Nauchnykh Seminarov POMI
%D 2019
%P 206-213
%V 480
%U http://geodesic.mathdoc.fr/item/ZNSL_2019_480_a14/
%G ru
%F ZNSL_2019_480_a14
N. A. Shirokov. Outer functions in classes of analytic functions of variable smoothness. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 47, Tome 480 (2019), pp. 206-213. http://geodesic.mathdoc.fr/item/ZNSL_2019_480_a14/

[1] N. A. Shirokov, Analytic functions smooth up to the boundary, Lecture Notes in Mathematics, 1312, Springer Verlag, 1988 ; 2013 | DOI | MR | Zbl

[2] N. A. Shirokov, “Vneshnie funktsii iz analiticheskikh klassov O. V. Besova”, Zap. nauchn. semin. POMI, 217, 1994, 172–217

[3] N. A. Shirokov, “Outer functions in yet another class of analytic functions”, Operator Theory: Advances and Applications, 113 (2000), 349–370 | MR | Zbl

[4] N. A. Shirokov, “Vnutrennie mnozhiteli analiticheskikh funktsii peremennoi gladkosti v zamknutom kruge”, Algebra i analiz

[5] A. V. Vasin, S. V. Kislyakov, A. N. Medvedev, “Lokalnaya gladkost analiticheskoi funktsii v sravnenii s gladkostyu ee modulya”, Algebra i analiz, 25:3 (2013), 52–85 | MR

[6] I. M. Vasilev, “O lokalnoi gladkosti analiticheskoi funktsii i ee modulya na granitse shara: anons”, Zap. nauchn. semin. POMI, 467, 2018, 30–33