A new computation of the Bergman kernel and related techniques

We introduce a technique for obtaining the Bergman kernel on certain Hartogs domains. To do so, we apply a differential operator to a known kernel function on a domain in lower dimensional space. We rediscover some known results and we obtain new explicit formulas. Using these formulas, we analyze the boundary behavior of the kernel function on the diagonal. Our technique also leads us to results about a cancellation of singularities for generalized hypergeometric functions and weighted Bergman kernels. Finally, we give an alternative approach to obtain explicit bases for complex harmonic homogeneous polynomial spaces

Zero products of Toeplitz operators on Reinhardt domains

Let $\Omega$ be a bounded Reinhardt domain in $\mathbb{C}^n$ and $\phi_1,\ldots,\phi_m$ be finite sums of bounded quasi-homogeneous functions. We show that if the product of Toeplitz operators $T_{\phi_m}\cdots T_{\phi_1}=0$ on the Bergman space on $\Omega$, then $\phi_j=0$ for some $j$.Comment: to appear in Can. Math. Bull., 11 page

A B\'{e}koll\`{e}-Bonami Class of Weights for Certain Pseudoconvex Domains

We prove the weighted $L^p$ regularity of the ordinary Bergman projection on certain pseudoconvex domains where the weight belongs to an appropriate generalization of the B\'{e}koll\`{e}-Bonami class. The main tools used are estimates on the Bergman kernel obtained by McNeal and B\'{e}koll\`{e}'s original approach of proving a good-lambda inequality.Comment: 24 page

Bekoll\'e-Bonami estimates on some pseudoconvex domains

We establish a weighted $L^p$ norm estimate for the Bergman projection for a class of pseudoconvex domains. We obtain an upper bound for the weighted $L^p$ norm when the domain is, for example, a bounded smooth strictly pseudoconvex domain, a pseudoconvex domain of finite type in $\mathbb C^2$, a convex domain of finite type in $\mathbb C^n$, or a decoupled domain of finite type in $\mathbb C^n$. The upper bound is related to the Bekoll\'e-Bonami constant and is sharp. When the domain is smooth, bounded, and strictly pseudoconvex, we also obtain a lower bound for the weighted norm.Comment: 28 pages. An application to the weak-type estimate is added as a new sectio