• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.85-103
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• 2015

We prove some sharp extremal distance results for functions in various spaces of analytic functions on bounded strictly pseudoconvex domains with smooth boundary. Also, we obtain atomic decompositions in multifunctional Bloch and weighted Bergman spaces of analytic functions on strictly pseudoconvex domains with smooth boundary, which extend known results in the classical case of a single function.

• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.323-331
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• 2022

In this paper, we present a formula for pseudohermitian curvatures on bounded strictly pseudoconvex domains in ℂ² with respect to the coefficients of adapted frames given by Graham and Lee in [3] and their structure equations. As an application, we will show that the pseudohermitian curvatures on strictly plurisubharmonic exhaustions of Thullen domains diverges when the points converge to a weakly pseudoconvex boundary point of the domain.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.223-228
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• 2015

In this paper, we study the eigenvalue problem of Schr$\ddot{o}$dinger-type operator on bounded domains in strictly pseudoconvex CR manifolds and obtain some universal inequalities for lower order eigenvalues. Moreover, we will give some generalized Reilly-type inequalities of the first nonzero eigenvalue of the sub-Laplacian on a compact strictly pseudoconvex CR manifold without boundary.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.81-87
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• 1996

We will construct polynomials of degree 6 in z and $\bar{z}$ on $C^2$ which gives, via its coefficient $\beta$ as a parameter, a family of pseudoconvex domains $\Omega_\beta$ in $C^2$ with the origin being a boundary point, and show that the domains $\Omega_\beta$ has no peak functions of class $c^1$ at the origin and has no holomorphic support functions for $1 \leq \beta < \frac{9}{5}$.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.753-762
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• 2012

We prove some sharp extremal distance results for functions in weighted Bergman spaces on the upper halfplane. We also prove new analogous results in the context of bounded strictly pseudoconvex domains with smooth boundary.