arXiv subjects

Kamthorn Chailuek

Publications and source records attributed to Kamthorn Chailuek.

2 recordsLinked to original sources

arXiv2009

Toeplitz operators on generalized Bergman spaces

We consider the weighted Bergman spaces HL^2(B^d,μ_λ), where dμ_λ(z)=c_λ(1-|z|^2)^lambda dτ, τbeing the hyperbolic volume measure. These spaces are nonzero if and only if λ>d. For 0<λ\leq d, spaces with the same formula for the reproducing kernel can be defined using a Sobolev-type norm. We define Toeplitz operators on these generalized Bergman spaces and investigate their properties. Specifically, we describe classes of symbols for which the corresponding Toeplitz operators can be defined as bounded operators or as a Hilbert--Schmidt operators on the generalized Bergman spaces.

math.CV↗

arXiv2003

A Pointwise Bound for a Holomorphic Function which is Square-Integrable with Respect to an Exponential Density Function

Let $ϕ$ be a real-valued smooth function on $\mathbf{C}$ satisfying $0 \le Δϕ\le M$ for some $M \ge 0$. We consider the space of all holomorphic functions which are square-integrable with respect to the measure $e^{-ϕ(z)} dz$. In this paper, a pointwise bound for any function in this space is established. We show that there exists a constant $K$ depending only on $M$ such that $|f(z)|^2 \le Ke^{ϕ(z)}\|f\|^2$ for any $f$ in this space and for any complex number $z$.

math.FA↗