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The Bergman projection on fat Hartogs triangles: L^p boundedness  [PDF]
L. D. Edholm,J. D. McNeal
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.
Weighted Bergman Projection on the Hartogs Triangle  [PDF]
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.
Weighted Sobolev regularity of the Bergman projection on the Hartogs triangle  [PDF]
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.
On the boundedness of Bergman projection  [PDF]
José ángel Peláez,Jouni R?tty?
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 $\int_{r}^1\omega(s)\,ds\le C\int_{\frac{1+r}{2}}^1\omega(s)\,ds$.
$L^p$ Mapping Properties of the Bergman Projection on the Hartogs Triangle  [PDF]
Debraj Chakrabarti,Yunus E. Zeytuncu
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
Boundedness of the Bergman projection on $L^p$ spaces with exponential weights  [PDF]
Olivia Constantin,Jose Angel Pelaez
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.
Regularity of Canonical Operators and Nebenhülle: Hartogs Domains  [PDF]
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.
Reproducing kernel estimates, bounded projections and duality on large weighted Bergman spaces  [PDF]
Hicham Arroussi,Jordi Pau
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.
Semi-norms of the Bergman projection  [PDF]
Marijan Markovic
Mathematics , 2014,
Abstract: It is known that the Bergman projection operator maps the space of essentially bounded functions in the unit ball in the d-dimensional complex vector space onto the Bloch space of the unit ball. This paper deals with the various semi-norms of the Bergman projection. We improve some recent results.
The Bergman kernels on Cartan-Hartogs domain
Weiping Yin
Chinese Science Bulletin , 1999, DOI: 10.1007/BF02887114
Abstract: The main point is the calculation of the Bergman kernel for the so-called Cartan-Hartogs domains. The Bergman kernels on four types of Cartan-Hartogs domains are given in explicit formulas. First by introducing the idea of semi-Reinhardt domain is given, of which the Cartan-Hartogs domains are a special case. Following the ideas developed in the classic monograph of Hua, the Bergman kernel for these domains is calculated. Along this way, the method of “inflation”, is made use of due to Boas, Fu and Straube.
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