The one-weight inequality for $\mathcal{H}$-harmonic Bergman projection
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915275265277952 |
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| author | Guo, Kunyu Wang, Zipeng Zhang, Kenan |
| author_facet | Guo, Kunyu Wang, Zipeng Zhang, Kenan |
| contents | Let $n\geqslant 3$ be an integer. For the Bekollé-Bonami weight $ω$ on the real unit ball $\mathbb{B}_n$, we obtain the following sharp one-weight estimate for the $\mathcal{H}$-harmonic Bergman projection: for $1<p<\infty$ and $-1<α<\infty$,
\[||P_α||_{ L^p(ωdν_α)\longrightarrow L^p(ωdν_α)}\leqslant C [ω]_{p,α}^{\max\left\{1,\frac{1}{p-1}\right\}},
\]
where $[ω]_{p,α}$ is the Bekollé-Bonami constant. Our proof is inspired by the dyadic harmonic analysis, and the key ingredient involves the discretization of the Bergman kernel for the $\mathcal{H}$-harmonic Bergman spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03106 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The one-weight inequality for $\mathcal{H}$-harmonic Bergman projection Guo, Kunyu Wang, Zipeng Zhang, Kenan Functional Analysis 42B20 Let $n\geqslant 3$ be an integer. For the Bekollé-Bonami weight $ω$ on the real unit ball $\mathbb{B}_n$, we obtain the following sharp one-weight estimate for the $\mathcal{H}$-harmonic Bergman projection: for $1<p<\infty$ and $-1<α<\infty$, \[||P_α||_{ L^p(ωdν_α)\longrightarrow L^p(ωdν_α)}\leqslant C [ω]_{p,α}^{\max\left\{1,\frac{1}{p-1}\right\}}, \] where $[ω]_{p,α}$ is the Bekollé-Bonami constant. Our proof is inspired by the dyadic harmonic analysis, and the key ingredient involves the discretization of the Bergman kernel for the $\mathcal{H}$-harmonic Bergman spaces. |
| title | The one-weight inequality for $\mathcal{H}$-harmonic Bergman projection |
| topic | Functional Analysis 42B20 |
| url | https://arxiv.org/abs/2505.03106 |