Composition and Volterra type operators on large Bergman spaces with rapidly decreasing weights
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| Format: | Preprint |
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2025
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| _version_ | 1866908460839337984 |
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| author | Almoka, M. Arroussi, H. Virtanen, J. |
| author_facet | Almoka, M. Arroussi, H. Virtanen, J. |
| contents | We characterize boundedness, compactness and Schatten class properties of generalized Volterra-type integral operators acting between large Bergman spaces $A_ω^p$ and $A_ω^q$ for $0 <p, q\leq \infty$. To prove our characterizations, which involve Berezin-type integral transforms, we use the Littlewood-Paley formula of Constantin and Peláez and corresponding embedding theorems. Our results generalize the work on integration operators of Pau and Peláez in J. Funct. Anal. 259 (2010), 2727--2756. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_16437 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Composition and Volterra type operators on large Bergman spaces with rapidly decreasing weights Almoka, M. Arroussi, H. Virtanen, J. Functional Analysis Complex Variables We characterize boundedness, compactness and Schatten class properties of generalized Volterra-type integral operators acting between large Bergman spaces $A_ω^p$ and $A_ω^q$ for $0 <p, q\leq \infty$. To prove our characterizations, which involve Berezin-type integral transforms, we use the Littlewood-Paley formula of Constantin and Peláez and corresponding embedding theorems. Our results generalize the work on integration operators of Pau and Peláez in J. Funct. Anal. 259 (2010), 2727--2756. |
| title | Composition and Volterra type operators on large Bergman spaces with rapidly decreasing weights |
| topic | Functional Analysis Complex Variables |
| url | https://arxiv.org/abs/2507.16437 |