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Generalized Volterra type integral operators on large Bergman spaces

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Arroussi, H., Gissy, H. and Virtanen, J. A. (2023) Generalized Volterra type integral operators on large Bergman spaces. Bulletin des Sciences Mathématiques. ISSN 0007-4497 doi: 10.1016/j.bulsci.2022.103226

Abstract/Summary

Let φ be an analytic self-map of the open unit disk D and g analytic in D. We characterize boundedness and compactness of generalized Volterra type integral operators GI(φ,g)f(z) = z0f (φ(ξ)) g(ξ) dξ and GV(φ,g)f(z) = z0f(φ(ξ)) g(ξ) dξ, acting between large Bergman spaces Apω and Aqω for 0 < p, q ≤ ∞. To prove our characterizations, which involve Berezin type integral transforms, we use the Littlewood-Paley formula of Constantin and Peláez and establish corresponding embedding theorems, which are also of independent interest.

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Item Type Article
URI https://reading-clone.eprints-hosting.org/id/eprint/109542
Identification Number/DOI 10.1016/j.bulsci.2022.103226
Refereed Yes
Divisions Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher Elsevier
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