The Bergman projection on fat Hartogs triangles: \(L^p\) boundedness (Q2790932)

The authors study the Bergman projection (the orthogonal projection from the square-integrable functions onto the subspace of square-integrable holomorphic functions) for domains in \(\mathbb{C}^2\) consisting of the points \((z_1,z_2)\) for which \(| z_1| ^k < | z_2| <1\), where \(k\)~is a positive integer. The case when \(k=1\) is the classical Hartogs triangle. The main result states that the Bergman projection for such a domain is bounded on the space \(L^p\) if and only if \((2k+2)/(k+2) < p < (2k+2)/k\). The proof depends on an explicit formula for the Bergman kernel function of such a domain computed by the first author [``Bergman theory of certain generalized Hartogs triangles'', Preprint, \url{arXiv:1504.07914}].