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 Mathematics , 2015, Abstract: A class of pseudoconvex domains in $\mathbb{C}^{n}$ generalizing the Hartogs triangle is considered. The $L^p$ boundedness of the Bergman projection associated to these domains is established, for a restricted range of $p$ depending on the "fatness" of domains. This range of $p$ is shown to be sharp.
 Liwei Chen Mathematics , 2014, Abstract: We prove the $L^p$ regularity of the weighted Bergman projection on the Hartogs triangle, where the weights are powers of the distance to the singularity at the boundary. The restricted range of $p$ is proved to be sharp. By using a two-weight inequality on the upper half plane with Muckenhoupt weights, we can consider a slightly wider class of weights.
 Liwei Chen Mathematics , 2015, Abstract: We prove a weighted Sobolev estimate of the Bergman projection on the Hartogs triangle, where the weight is some power of the distance to the singularity at the boundary. This method also applies to the $n$-dimensional generalization of the Hartogs triangle.
 Mathematics , 2015, Abstract: The main purpose of this survey is to gather results on the boundedness of the Bergman projection. First, we shall go over some equivalent norms on weighted Bergman spaces $A^p_\omega$ which are useful in the study of this question. In particular, we shall focus on a decomposition norm theorem for radial weights~$\omega$ with the doubling property $\int_{r}^1\omega(s)\,ds\le C\int_{\frac{1+r}{2}}^1\omega(s)\,ds$.
 Mathematics , 2014, Abstract: We prove optimal estimates for the mapping properties of the Bergman projection on the Hartogs triangle in weighted $L^p$ spaces when $p>\frac{4}{3}$, where the weight is a power of the distance to the singular boundary point. For $1  Mathematics , 2013, Abstract: Let$v(r)=\exp\left(-\frac{\alpha}{1-r}\right)$with$\alpha>0$, and let$\mathbb{D}$be the unit disc in the complex plane. Denote by$A^p_v$the subspace of analytic functions of$L^p(\mathbb{D},v)$and let$P_v$be the orthogonal projection from$L^2(\mathbb{D},v)$onto$A^2_v$. In 2004, Dostanic revealed the intriguing fact that$P_v$is bounded from$L^p(\mathbb{D},v)$to$A^p_v$only for$p=2$, and he posed the related problem of identifying the duals of$A^p_v$for$p\ge 1$,$p\neq 2$. In this paper we propose a solution to this problem by proving that$P_v$is bounded from$\,L^p(\D,v^{p/2})$to$A^p_{v^{p/2}}$whenever$1\le p <\infty$, and, consequently, the dual of$A^p_{v^{p/2}}$for$p\ge 1$can be identified with$A^{q}_{v^{q/2}}$, where$1/p+1/q=1$. In addition, we also address a similar question on some classes of weighted Fock spaces.  Yunus E. Zeytuncu Mathematics , 2013, Abstract: We relate the regularity of the Bergman projection operator and the canonical solution operator to the Nebenh\"ulle of complete Hartogs domains.  Mathematics , 2013, Abstract: We obtain ceratin estimates for the reproducing kernels of large weighted Bergman spaces. Applications of these estimates to boundedness of the Bergman projection on$L^p(\D,\omega ^{p/2})\$, complex interpolation and duality of weighted Bergman spaces are given.