Weighted estimates for the Bergman projection on planar domains
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929364889763840 |
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| author | Green, A. Walton Wagner, Nathan A. |
| author_facet | Green, A. Walton Wagner, Nathan A. |
| contents | We investigate weighted Lebesgue space estimates for the Bergman projection on a simply connected planar domain via the domain's Riemann map. We extend the bounds which follow from a standard change-of-variable argument in two ways. First, we provide a regularity condition on the Riemann map, which turns out to be necessary in the case of uniform domains, in order to obtain the full range of weighted estimates for the Bergman projection for weights in a Békollè-Bonami-type class. Second, by slightly strengthening our condition on the Riemann map, we obtain the weighted weak-type $(1,1)$ estimate as well. Our proofs draw on techniques from both conformal mapping and dyadic harmonic analysis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_15754 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weighted estimates for the Bergman projection on planar domains Green, A. Walton Wagner, Nathan A. Complex Variables Classical Analysis and ODEs Primary: 30H20, 42B20. Secondary: 30C20 We investigate weighted Lebesgue space estimates for the Bergman projection on a simply connected planar domain via the domain's Riemann map. We extend the bounds which follow from a standard change-of-variable argument in two ways. First, we provide a regularity condition on the Riemann map, which turns out to be necessary in the case of uniform domains, in order to obtain the full range of weighted estimates for the Bergman projection for weights in a Békollè-Bonami-type class. Second, by slightly strengthening our condition on the Riemann map, we obtain the weighted weak-type $(1,1)$ estimate as well. Our proofs draw on techniques from both conformal mapping and dyadic harmonic analysis. |
| title | Weighted estimates for the Bergman projection on planar domains |
| topic | Complex Variables Classical Analysis and ODEs Primary: 30H20, 42B20. Secondary: 30C20 |
| url | https://arxiv.org/abs/2309.15754 |