Products of multiplication, composition and differentiation between weighted Bergman-Nevanlinna and Bloch-type spaces

Authors

AJAY K. SHARMA

DOI

10.3906/mat-0806-24

Abstract

Let \varphi and \psi be holomorphic maps on D such that \varphi ( D ) \subset D . Let C_{\varphi} , M_{\psi} and D be the composition, multiplication and differentiation operators, respectively. In this paper, we consider linear operators induced by products of these operators from Bergman-Nevanlinna spaces A^{\beta}_N to Bloch-type spaces. In fact, we prove that these operators map A^{\beta}_N compactly into Bloch-type spaces if and only if they map A^{\beta}_N boundedly into these spaces.

Keywords

Composition operator, Multiplication operator, Differentiation operator, Bergman space, Bloch space, Growth space

First Page

275

Last Page

291

Recommended Citation

SHARMA, AJAY K. (2011) "Products of multiplication, composition and differentiation between weighted Bergman-Nevanlinna and Bloch-type spaces," Turkish Journal of Mathematics: Vol. 35: No. 2, Article 9. https://doi.org/10.3906/mat-0806-24
Available at: https://journals.tubitak.gov.tr/math/vol35/iss2/9