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In this paper we give sharp $L_p$ Markov type inequalities for derivatives of multivariate polynomials for a wide family of UPC domains., Comment: early-stage research, comments are welcome

The purpose of this paper is to study a Markov type inequality for algebraic polynomials in $L^p$ norm on two-dimensional cuspidal domains., Comment: all comments are welcome

We provide a sufficient condition for the compactness of a Toeplitz operator acting on the Segal-Bargmann space of vector-valued functions written in terms of an associated operator-valued kernel., Comment: 11 pages

Let $\Omega=\{(x,y) \in \mathbb{R}^2 : |x|4y\}$. We prove that the optimal exponent in Markov's inequality on $\Omega$ in $L^p$ norms is 4., Comment: all comments are welcome

It is known that for $C^{\infty}$ determining sets Markov's property is equivalent to Bernstein's property. The purpose of this paper is to prove an analogous result in the case of compact subsets of algebraic varieties., Comment: 11 pages

The purpose of this paper is to give an estimate of the $L^p$-norm of the Bergman projection on the Hartogs triangle., Comment: 12 pages, all comments are welcome!

In this paper we investigate a two classes of domains in $\mathbb{C}^n$ generalizing the Hartogs triangle. We prove optimal estimates for the mapping properties of the Bergman projection on these domains., Comment: 6 pages, All comments and remarks are welcome

Let $\Omega$ be an arbitrary bounded semi-Reinhardt domain in $\mathbb{C}^{m+n}$. We show that for $m \geq 2$, if a Hankel operator with an anti-holomorphic symbol is Hilbert-Schmidt on the Bergman space $L_a^2(\Omega)$, then it must equal zero. This fact has previously been proved for Reinhardt domains., Comment: This paper has been withdrawn by the authors due to mistake in the proof of Main theorem

In this paper we investigate the Bergman kernel function for intersection of two complex ellipsoids $\{(z,w_1,w_2) \in \mathbb{C}^{n+2} : |z_1|^2 + \cdots + |z_n|^2 + |w_1|^q < 1, \quad |z_1|^2 + \cdots + |z_n|^2 + |w_2|^r < 1\}.$, Comment: 11 pages

In this paper We investigate the Lu Qi-Keng problem for intersection of two complex ellipsoids $\{z \in \mathbb{C}^3 \colon |z_1|^2 + |z_2|^q < 1, \quad |z_1|^2 + |z_3|^r < 1\}$., Comment: 9 pages

In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for intersection of two complex ellipsoids $\{z \in \mathbb{C}^3 \colon |z_1|^p + |z_2|^q < 1, \quad |z_1|^p + |z_3|^r < 1\}$. We consider cases $p=6, q= r= 2$ and $p=q=r=2$. We also investigate the Lu Qi-Keng problem for $p=q=r=2$., Comment: 19 pages. arXiv admin note: text overlap with arXiv:0810.2632 by other authors

In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for Reinhardt domains $\{|z_3|^{\lambda} < |z_1|^{2p} + |z_2|^2, \quad |z_1|^{2p} + |z_2|^2 < |z_1|^{p} \}$ and $\{|z_4|^{\lambda} < (|z_1|^2 + |z_2|^2)^{p} + |z_3|^2, \quad (|z_1|^2 + |z_2|^2)^{p} + |z_3|^2 < (|z_1|^2 + |z_2|^2 )^{p/2} \}$., Comment: 9 pages