Bergman kernels of elementary Reinhardt domains

Chakrabarti, Debraj; Konkel, Austin; Mainkar, Meera; Miller, Evan

doi:10.2140/pjm.2020.306.67

Cited by 11 publications

(3 citation statements)

References 22 publications

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“…In the former case, we decompose A 2 Ω n+1 γ to obtain an estimate of the Bergman kernel. For more discussion of the Bergman kernel, see [11,15,16]. We then use Schur's lemma to discuss the boundedness of the projection operator.…”

Section: Introductionmentioning

confidence: 99%

$L^p$ boundedness of the Bergman Projection on generalizations of the Hartogs triangle in $\mathbb{C}^{n+1}$

Fu¹,

Deng²

2022

Preprint

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Section: Introductionmentioning

confidence: 99%

$L^p$ boundedness of the Bergman Projection on generalizations of the Hartogs triangle in $\mathbb{C}^{n+1}$

Fu¹,

Deng²

2022

Preprint

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“…Let be an n -tuple of positive integers. The domain was introduced in [CKMM20] where it was called an elementary Reinhardt domain of signature 1 , and its Bergman kernel was computed explicitly. We see that is a monomial polyhedron as in (1.1), since …”

Section: Introductionmentioning

confidence: 99%

-regularity of the Bergman projection on quotient domains

Bender¹,

Chakrabarti²,

Edholm³

et al. 2021

Can. J. Math.-J. Can. Math.

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We obtain sharp ranges of L p -boundedness for domains in a wide class of Reinhardt domains representable as sub-level sets of monomials, by expressing them as quotients of simpler domains. We prove a general transformation law relating L pboundedness on a domain and its quotient by a finite group. The range of p for which the Bergman projection is L p -bounded on our class of Reinhardt domains is found to shrink as the complexity of the domain increases. This is a ``preproof'' accepted article for Canadian Journal of Mathematics This version may be subject to change during the production process.

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“…Since the work of D'Angelo [6], many authors have contributed explicit calculations of Bergman kernels. We refer the reader to [7,2,21,17,3] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Algebraic Bergman kernels and finite type domains in $\mathbb{C}^2$

Ebenfelt¹,

Xiao²,

Xu³

2021

Preprint

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Let G ⊂ C 2 be a smoothly bounded pseudoconvex domain and assume that the Bergman kernel of G is algebraic of degree d. We show that the boundary ∂G is of finite type and the type r satisfies r ≤ 2d. The inequality is optimal as equality holds for the egg domains {|z| 2 + |w| 2s < 1}, s ∈ Z+, by D'Angelo's explicit formula for their Bergman kernels. Our results imply, in particular, that a smoothly bounded pseudoconvex domain G ⊂ C 2 cannot have rational Bergman kernel unless it is strongly pseudoconvex and biholomorphic to the unit ball by a rational map. Furthermore, we show that if the Bergman kernel of G is rational of the form p q , reduced to lowest degrees, then its rational degree max{deg p, deg q} ≥ 6. Equality is achieved if and only if G is biholomorphic to the unit ball by a complex affine transformation of C 2 .

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Bergman kernels of elementary Reinhardt domains

Cited by 11 publications

References 22 publications

$L^p$ boundedness of the Bergman Projection on generalizations of the Hartogs triangle in $\mathbb{C}^{n+1}$

$L^p$ boundedness of the Bergman Projection on generalizations of the Hartogs triangle in $\mathbb{C}^{n+1}$

-regularity of the Bergman projection on quotient domains

Algebraic Bergman kernels and finite type domains in $\mathbb{C}^2$

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