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Normal weighted Bergman type operators on mixed norm spaces over the ball in $\mathbb C^n$

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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.

Abstract

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.

참고문헌 (24)

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