Boundedness of Multiparameter Forelli-Rudin Type Operators on Product $L^p$ Spaces over Tubular Domains
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913381483544576 |
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| author | Li, Lvchang Liang, Yuheng Li, Haichou |
| author_facet | Li, Lvchang Liang, Yuheng Li, Haichou |
| contents | In this paper, we introduce and study two classes of multiparameter Forelli-Rudin type operators from $L^{\vec{p}}\left(T_B\times T_B, dV_{α_1}\times dV_{α_2}\right)$ to $L^{\vec{q}}\left(T_B\times T_B, dV_{β_1}\times dV_{β_2}\right)$, especially on their boundedness, where $L^{\vec{p}}\left(T_B\times T_B, dV_{α_1}\times dV_{α_2}\right)$ and $L^{\vec{q}}\left(T_B\times T_B, dV_{β_1}\times dV_{β_2}\right)$ are both weighted Lebesgue spaces over the Cartesian product of two tubular domains $T_B\times T_B$, with mixed-norm and appropriate weights. We completely characterize the boundedness of these two operators when $1\le \vec{p}\le \vec{q}<\infty$. Moreover, we provide the necessary and sufficient condition of the case that $\vec{q}=(\infty,\infty)$. As an application, we obtain the boundedness of three common classes of integral operators, including the weighted multiparameter Bergman-type projection and the weighted multiparameter Berezin-type transform. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_04810 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundedness of Multiparameter Forelli-Rudin Type Operators on Product $L^p$ Spaces over Tubular Domains Li, Lvchang Liang, Yuheng Li, Haichou Functional Analysis In this paper, we introduce and study two classes of multiparameter Forelli-Rudin type operators from $L^{\vec{p}}\left(T_B\times T_B, dV_{α_1}\times dV_{α_2}\right)$ to $L^{\vec{q}}\left(T_B\times T_B, dV_{β_1}\times dV_{β_2}\right)$, especially on their boundedness, where $L^{\vec{p}}\left(T_B\times T_B, dV_{α_1}\times dV_{α_2}\right)$ and $L^{\vec{q}}\left(T_B\times T_B, dV_{β_1}\times dV_{β_2}\right)$ are both weighted Lebesgue spaces over the Cartesian product of two tubular domains $T_B\times T_B$, with mixed-norm and appropriate weights. We completely characterize the boundedness of these two operators when $1\le \vec{p}\le \vec{q}<\infty$. Moreover, we provide the necessary and sufficient condition of the case that $\vec{q}=(\infty,\infty)$. As an application, we obtain the boundedness of three common classes of integral operators, including the weighted multiparameter Bergman-type projection and the weighted multiparameter Berezin-type transform. |
| title | Boundedness of Multiparameter Forelli-Rudin Type Operators on Product $L^p$ Spaces over Tubular Domains |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2406.04810 |