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NORMAL WEIGHTED BERGMAN TYPE OPERATORS ON MIXED NORM SPACES OVER THE BALL IN ℂ<sup>n</sup>
Avetisyan, Karen L.,Petrosyan, Albert I. Korean Mathematical Society 2018 대한수학회지 Vol.55 No.2
The paper studies some new ${\mathbb{C}}^n$-generalizations of Bergman type operators introduced by Shields and Williams depending on a normal pair of weight functions. We find the values of parameter ${\beta}$ for which these operators are bounded on mixed norm spaces L(p, q, ${\beta}$) over the unit ball in ${\mathbb{C}}^n$. Moreover, these operators are bounded projections as well, and the images of L(p, q, ${\beta}$) under the projections are found.
Normal weighted Bergman type operators on mixed norm spaces over the ball in $\mathbb C^n$
Karen L. Avetisyan,Albert I. Petrosyan 대한수학회 2018 대한수학회지 Vol.55 No.2
The paper studies some new $\mathbb C^n$-generalizations of Bergman type operators introduced by Shields and Williams depending on a normal pair of weight functions. We find the values of parameter $\beta$ for which these operators are bounded on mixed norm spaces $L(p,q,\beta)$ over the unit ball in $\mathbb C^n$. Moreover, these operators are bounded projections as well, and the images of $L(p,q,\beta)$ under the projections are found.