Geodesic
On new decomposition theorems in some analytic function spaces in bounded pseudoconvex domains
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 4, pp. 503-514

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

We provide new sharp decomposition theorems for multifunctional Bergman spaces in the unit ball and bounded pseudoconvex domains with smooth boundary expanding known results from the unit ball. Namely we prove that $ \prod \limits_{j=1}^{m}||f_{j}|| _{X_{j}} \asymp ||f_{1} \dots f_{m}||_{A_{\alpha}^{p}}$ for various $(X_{j})$ spaces of analytic functions in bounded pseudoconvex domains with smooth boundary where $f, f_{j}, j=1,\dots, m$ are analytic functions and where $A_{\alpha}^{p}, 0 $ is a Bergman space. This in particular also extend in various directions a known theorem on atomic decomposition of Bergman $A^{p}_{\alpha}$ spaces.
Keywords: unit ball, Bergman spaces, decomposition theorems, Hardy type spaces.
Mots-clés : pseudoconvex domains 
@article{JSFU_2020_13_4_a11,
     author = {Romi F. Shamoyan and Elena B. Tomashevskaya},
     title = {On new decomposition theorems in some analytic function spaces in bounded pseudoconvex domains},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {503--514},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_4_a11/}
}
TY  - JOUR
AU  - Romi F. Shamoyan
AU  - Elena B. Tomashevskaya
TI  - On new decomposition theorems in some analytic function spaces in bounded pseudoconvex domains
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2020
SP  - 503
EP  - 514
VL  - 13
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2020_13_4_a11/
LA  - en
ID  - JSFU_2020_13_4_a11
ER  - 
%0 Journal Article
%A Romi F. Shamoyan
%A Elena B. Tomashevskaya
%T On new decomposition theorems in some analytic function spaces in bounded pseudoconvex domains
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2020
%P 503-514
%V 13
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2020_13_4_a11/
%G en
%F JSFU_2020_13_4_a11
Romi F. Shamoyan; Elena B. Tomashevskaya. On new decomposition theorems in some analytic function spaces in bounded pseudoconvex domains. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 4, pp. 503-514. http://geodesic.mathdoc.fr/item/JSFU_2020_13_4_a11/