Geodesic
Factorization theorems for some spaces of analytic functions
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2006), pp. 124-127 
R. F. Shamoyan. Factorization theorems for some spaces of analytic functions. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2006), pp. 124-127. http://geodesic.mathdoc.fr/item/BASM_2006_3_a13/
@article{BASM_2006_3_a13,
     author = {R. F. Shamoyan},
     title = {Factorization theorems for some spaces of analytic functions},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {124--127},
     year = {2006},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2006_3_a13/}
}
TY  - JOUR
AU  - R. F. Shamoyan
TI  - Factorization theorems for some spaces of analytic functions
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2006
SP  - 124
EP  - 127
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/BASM_2006_3_a13/
LA  - en
ID  - BASM_2006_3_a13
ER  - 
%0 Journal Article
%A R. F. Shamoyan
%T Factorization theorems for some spaces of analytic functions
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2006
%P 124-127
%N 3
%U http://geodesic.mathdoc.fr/item/BASM_2006_3_a13/
%G en
%F BASM_2006_3_a13

Voir la notice de l'article provenant de la source Math-Net.Ru

We provide several factorization theorems for different subspaces of the space of all analytic functions in the unit disk, in particular we prove a strong factorization theorem for Classical Hardy classes with Muckenhoupt weights. Proofs are based on a new weighted version of Coifman–Meyer–Stein theorem on factorization of tent spaces and on properties of an extremal outher function,which was constructed by E. Dynkin

[1] Gorowitz Ch., “Factorization theorems for functions in the Bergman space”, Duke Math. Journal, 44 (1977), 201–213 | DOI | MR

[2] Cohn W., “A factorization theorem for the derivative of a function on $H^p$”, Proc. AMS, 127:2 (1999), 509–517 | DOI | MR | Zbl

[3] Cohn W., Verbitsky I., “Factorization of Tent spaces and Hankel operators”, Journal of Functional Analysis, 175 (2000), 308–329 | DOI | MR | Zbl

[4] Coifman R., Meyer Y., Stein E., “Some new functional spaces and their application to harmonic analysis”, Journal of Functional Analysis, 1985, 304–335 | MR | Zbl

[5] Grafakos L., Classical and Modern Fourier Analysis, Prentice Hall, 2003 | MR

[6] Dynkin E., “Sets of Free interpolation for Hoelder classes”, Mat. Sbornik, 109:1 (1979), 107–128 | MR