Absolutely summing Hankel operators on Bergman spaces
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918219399299072 |
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| author | Fan, Zhijie He, Bo Wang, Xiaofeng Zeng, Zhicheng |
| author_facet | Fan, Zhijie He, Bo Wang, Xiaofeng Zeng, Zhicheng |
| contents | In this paper we initiate the study of absolute summability for big and little Hankel operators $
H_f^β,h_f^β:A_α^p(\mathbb{B}_n)\to L^q(\mathbb{B}_n,dv_β), $
acting between weighted Bergman and weighted Lebesgue spaces on the unit ball, for possibly different integrability exponents $p$ and $q$. We characterize those symbols $f$ for which the big Hankel operator $H_f^β$ is $r$-summing, and those for which the little Hankel operator $h_f^β$ is $r$-summing. Our approach relies on a deep revisit of the absolute summability of the associated Carleson embedding operators from $A_α^p(\mathbb{B}_n)$ to $L^q(\mathbb{B}_n,dv_β)$, from which we obtain characterizations of absolutely summing big and little Hankel operators that appear to be new even in the diagonal case $p=q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22165 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Absolutely summing Hankel operators on Bergman spaces Fan, Zhijie He, Bo Wang, Xiaofeng Zeng, Zhicheng Functional Analysis 47B35, 47B10, 30H20 In this paper we initiate the study of absolute summability for big and little Hankel operators $ H_f^β,h_f^β:A_α^p(\mathbb{B}_n)\to L^q(\mathbb{B}_n,dv_β), $ acting between weighted Bergman and weighted Lebesgue spaces on the unit ball, for possibly different integrability exponents $p$ and $q$. We characterize those symbols $f$ for which the big Hankel operator $H_f^β$ is $r$-summing, and those for which the little Hankel operator $h_f^β$ is $r$-summing. Our approach relies on a deep revisit of the absolute summability of the associated Carleson embedding operators from $A_α^p(\mathbb{B}_n)$ to $L^q(\mathbb{B}_n,dv_β)$, from which we obtain characterizations of absolutely summing big and little Hankel operators that appear to be new even in the diagonal case $p=q$. |
| title | Absolutely summing Hankel operators on Bergman spaces |
| topic | Functional Analysis 47B35, 47B10, 30H20 |
| url | https://arxiv.org/abs/2511.22165 |