Geodesic
On some new estimates for integrals of the square function and analytic Bergman type classes in some domains in $C^n$
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 31 (2020) no. 2, pp. 32-55 Cet article a éte moissonné depuis la source Math-Net.Ru

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В работе приведены новые эквивалентные квазинормы для некоторых новых пространств типа Бергмана в полидиске и в ограниченных псевдовыпуклых областях. Подобные оценки установлены также для классов типа Харди в полидиске. Эти результаты обобщают некоторые известные одномерные неравенства для пространств типа Харди и классов типа Бергмана в единичном круге на случай полидиска и ограниченной псевдовыпуклой области. Оценки такого типа могут иметь также различные приложения. Пусть $D$ ограниченная или неограниченная область в $C^n$ (ограниченная псевдовыпуклая или неограниченная трубчатая область над симметрическим конусом). Подходы, примененные в данной работе при доказательстве утверждений в полидиске могут быть, по-видимому, также использованы для доказательства подобных приведенных в данной работе оценок, но в полиобластях $D\times\cdots\times D$ существенно более общего типа, чем единичный полидиск
Keywords: polydisk, integral operators, analytic functions, analytic spaces, Hardy class, new Bergman space
Mots-clés : pseudoconvex domains. 
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     title = {On some new estimates for integrals of the square function and analytic {Bergman} type classes in some domains in $C^n$},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {32--55},
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R. F. Shamoyan; E. B. Tomashevskaya. On some new estimates for integrals of the square function and analytic Bergman type classes in some domains in $C^n$. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 31 (2020) no. 2, pp. 32-55. http://geodesic.mathdoc.fr/item/VKAM_2020_31_2_a2/

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