Logarithmic Bergman-type space and a sum of product-type operators

Abstract

One of the aims of the present paper is to obtain some properties about logarithmic Bergman-type space on the unit ball. As some applications, the bounded and compact operators $ \mathfrak{S}^m_{\vec{u}, {\varphi}} = \sum_{i = 0}^{m}M_{u_i}C_{\varphi}\Re^{i} $ from logarithmic Bergman-type space to weighted-type space on the unit ball are completely characterized.

Keywords

• product-type operator
• boundedness
• compactness
• logarithmic bergman-type space
• weighted-type space