On new decomposition theorems in some analytic function spaces in bounded pseudoconvex domains

Romi F. Shamoyan ; Elena B. Tomashevskaya

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 4, pp. 503-514

Résumé

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.

Détail

Keywords: unit ball, Bergman spaces, decomposition theorems, Hardy type spaces.
Mots-clés : pseudoconvex domains