Bergman theory of certain generalized Hartogs triangles

Abstract

The Bergman theory of domains $\{|z_1{|}^{\gamma }<|z_2|<1\}$ in ${\mathbb{C}}^2$ is studied for certain values of $\gamma$, including all positive integers. For such $\gamma$, we obtain a closed form expression for the Bergman kernel, ${\mathbb{B}}_{\gamma }$. With these formulas, we make new observations relating to the Lu Qi-Keng problem and analyze the boundary behavior of ${\mathbb{B}}_{\gamma }(z,z)$.

13 pages

References in corpus (1)

• The Bergman projection on fat Hartogs triangles: L^p boundedness

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