Generalized Composition Operators from ℬ μ Spaces to Q K , ω ( p , q ) Spaces

Haiying Li; Tianshui Ma

doi:10.1155/2014/897389

2014 Generalized Composition Operators from

{\scr B}_{\mu }

Spaces to

{Q}_{K,\omega }(p,q)

Spaces

Haiying Li, Tianshui Ma

Abstr. Appl. Anal. 2014(SI43): 1-6 (2014). DOI: 10.1155/2014/897389

Abstract

Let $0<p<\infty$ , let $-2<q<\infty$ , and let $\phi$ be an analytic self-map of $\mathrm{\Bbb D}$ and $g\in H(\mathrm{\Bbb D})$ . The boundedness and compactness of generalized composition operators $({C}_{\phi }^{g}f)(z)={\int }_{0}^{z}\mathrm{‍}{f}^{\mathrm{\text{'}}}(\phi (\xi ))g(\xi )d\xi , z\in \mathrm{\Bbb D}, f\in H(\mathrm{\Bbb D})$ , from ${\scr B}_{\mu }$ ( ${\scr B}_{\mu ,0}$ ) spaces to ${Q}_{K,\omega }(p,q)$ spaces are investigated.

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Haiying Li and Tianshui Ma "Generalized Composition Operators from