Area functions characterizations of weighted Bergman spaces

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• 作者：Marcos Ló ; pez-Garcí ; a ^{flopez@matem.unam.mx" class="auth_mail" title="E-mail the corresponding author} ; Carmen Lozano¹ ; ^{carmenlozano@im.unam.mx" class="auth_mail" title="E-mail the corresponding author} ; Salvador Pé ; rez-Esteva ; ² ; ^{spesteva@im.unam.mx" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Weighted Bergman spaces ; Area functions
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：447
• 期：1
• 页码：529-541
• 全文大小：319 K

文摘

The aim of this paper is to find weights W   in the unit ball of Cⁿ${\mathbb{C}}^n$ for which characterization of the area integrals of Bergman spaces A^p(W)$A^p(W)$ holds. The area functions, related to those used to describe Hardy spaces, involve the radial derivative, the complex gradient and the invariant gradient. We extend to certain Bekollé weights the characterization by Z. Chen and W. Ouyang of the Bergman spaces with the classical weights W(z)=(1−|z|)^α$W(z)={(1-|z|)}^{\alpha }$ using area functions.