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Inyoung Park

Publications and source records attributed to Inyoung Park.

6 recordsLinked to original sources
arXiv2024

Kernel-induced distance and its applications to Composition operators on Large Bergman spaces

In this paper, we obtain a complete characterization for the compact difference of two composition operators acting on Bergman spaces with a rapidly decreasing weight $\omega=e^{-\eta}$, $\Delta\eta>0$. In addition, we provide simple inducing maps which support our main result. We also study the topological path connected component of the space of all bounded composition operators on $A^2(\omega)$ endowed with the Hilbert-Schmidt norm topology.

math.FA↗
arXiv2021

Difference of Composition operators over Bergman spaces with exponential weights

In this paper, we obtain a complete characterization for the compact difference of two composition operators acting on Bergman spaces with weight $\omega=e^{-\eta}$, $\Delta\eta>0$ in terms of the $\eta$-derived pseudodistance of two analytic self maps. In addition, we provide simple inducing maps which support our main result. We also study the topological path component of the space of all bounded composition operators on $A^2(\omega)$ endowed with the Hilbert-Schmidt norm topology.

math.FA↗
arXiv2019

Compact differences of composition operators on large weighted Bergman spaces

While there have been extensive studies regarding the theory of composition operators in standard Bergman spaces, there have not been many results pertaining to large Bergman spaces due to a lack of useful tools. In this paper, we give the characterizations of the compact differences of composition operators in Bergman spaces with the exponential type weight using a newly defined Riemannian distance. Furthermore, we give a sufficient condition for the question when two composition operators lie in the same component.

math.FA↗
arXiv2017

The weighted composition operators on the large weighted Bergman spaces

In this paper, we characterize bounded, compact or Schatten class weighted composition operators acting on Bergman spaces with the exponential type weights. Moreover, we give the proof of the necessary part for the boundedness of composition operators on large weighted Bergman spaces given by Kriete and Maccluer in 1992.

math.FA↗
arXiv2014

Positive Toeplitz operators on Large Bergman spaces in the unit disk

We study positive Toeplitz operators on the Bergman spaces having the fast decreasing weight functions in a certain class. We give the characterizations for the boundedness and compactness of Toeplitz operators in terms of their Berezin transforms and averaging functions. In particular, we show the equivalent conditions in order that Toeplitz operators on $A^2(ω)$ belong to the Schatten class $S_p$, $0<p<\infty$.

math.FA↗