Weighted theory of Toeplitz operators on the Bergman space

Stockdale, Cody B.; Wagner, Nathan A.

doi:10.1007/s00209-023-03347-x

Math. Z.

2023

DOI: 10.1007/s00209-023-03347-x

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Weighted theory of Toeplitz operators on the Bergman space

Cody B. Stockdale,

Nathan A. Wagner

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2024

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Weighted estimates for the Bergman projection on planar domains

Green,

Wagner

2024

Trans. Amer. Math. Soc.

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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.

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Weighted estimates for the Bergman projection on planar domains

Green,

Wagner

2024

Trans. Amer. Math. Soc.

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Weighted theory of Toeplitz operators on the Bergman space

Cited by 1 publication

References 33 publications

Weighted estimates for the Bergman projection on planar domains

Weighted estimates for the Bergman projection on planar domains

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