On New Decomposition Theorems in some Analytic Function Spaces in Bounded Pseudoconvex Domains
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https://elib.sfu-kras.ru/handle/2311/135385Author:
Shamoyan, Romi F.
Tomashevskaya, Elena B.
Шамоян, Роми Ф.
Томашевская, Елена В.
Date:
2020-08Journal Name:
Журнал Сибирского федерального университета.Математика и физика.Journal of Siberian Federal University. Mathematics & Physics, 2020 13 (4)Abstract:
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
mΠ
j=1
jjfj jjXj
≍ jjf1 : : : fmjj
Ap
for various (Xj) spaces of analytic functions in
bounded pseudoconvex domains with smooth boundary where f; fj ; j = 1; : : : ;m are analytic functions
and where Ap
; 0 < p < 1; > �����1 is a Bergman space. This in particular also extend in various
directions a known theorem on atomic decomposition of Bergman Ap
spaces. Мы даем новые точные теоремы разложения для многофункциональных пространств
Бергмана в единичном шаре и ограниченных псевдовыпуклых областей с гладкой границей, рас-
ширяющей известные результаты из единичного шара.
А именно мы докажем, что
mΠ
j=1
jjfj jjXj
≍ jjf1 : : : fmjj
Ap
для различных (Xj) пространства ана-
литических функций в ограниченных псевдовыпуклых областях с гладкой границей, где f; fj ,
j = 1; : : : ;m — аналитические функции, а Ap
; 0 < p < 1; >1 — пространство Бергмана. Это,
в частности, также расширяет в разных направлениях известную теорему об атомном разложении
пространств Ap
Бергмана
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