• Journal of the Korean Mathematical Society
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• v.37 no.4
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• pp.531-544
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• 2000

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.621-626
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• 2001

Let { $A_{>o}$ t= exp(M log t)} $_{t}$ be a dilation group where M is a real n$\times$n matrix whose eigenvalues has strictly positive real part, and let $\rho$be an $A_{t}$ -homogeneous distance function defined on ( $R^{n}$ ). Suppose that K is a function defined on ( $R^{n}$ ) such that /K(x)/$\leq$ (No Abstract.see full/text) for a decreasing function defined on (t) on R+ satisfying where wo(x)=│log│log (x)ll. For f$\in$ $L_{1}$ ( $R^{n}$ ), define f(x)=sup t>0 Kt*f(x)=t-v K(Al/tx) and v is the trace of M. Then we show that \ulcorner is a bounded operator of $L_{-{1}( $R^{n}$ ) into $L^1$,$\infty$( $R^{n}$).

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1509-1533
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• 2020

We provide detailed proofs for local gradient estimates for elliptic equations in divergence form with partial Dini mean oscillation coefficients in a ball and a half ball.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1791-1809
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• 2018

Let T be the singular integral operator with nonsmooth kernel which was introduced by Duong and McIntosh, and $T_q(q{\in}(1,{\infty}))$ be the vector-valued operator defined by $T_qf(x)=({\sum}_{k=1}^{\infty}{\mid}T\;f_k(x){\mid}^q)^{1/q}$. In this paper, by proving certain weak type endpoint estimate of L log L type for the grand maximal operator of T, the author establishes some quantitative weighted bounds for $T_q$ and the corresponding vector-valued maximal singular integral operator.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.239-263
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• 2019

The $Calder{\acute{o}}n$-Zygmund type estimate is proved for elliptic obstacle problems in bounded non-smooth domains. The problems are related to divergence form nonlinear elliptic equation with measurable nonlinearities. Precisely, nonlinearity $a({\xi},x_1,x^{\prime})$ is assumed to be only measurable in one spatial variable $x_1$ and has locally small BMO semi-norm in the other spatial variables x', uniformly in ${\xi}$ variable. Regarding non-smooth domains, we assume that the boundaries are locally flat in the sense of Reifenberg. We also investigate global regularity in the settings of weighted Orlicz spaces for the weak solutions to the problems considered here.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.809-822
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• 2007

Certain weak type endpoint estimates are established for maximal commutators generated by $Calder\acute{o}n-Zygmund$ operators and $Osc_{exp}L^{\gamma}({\mu})$ functions for ${\gamma}{\ge}1$ under the condition that the underlying measure only satisfies some growth condition, where the kernels of $Calder\acute{o}n-Zygmund$ operators only satisfy the standard size condition and some $H\ddot{o}rmander$ type regularity condition, and $Osc_{exp}L^{\gamma}({\mu})$ are the spaces of Orlicz type satisfying that $Osc_{exp}L^{\gamma}({\mu})$ = RBMO(${\mu}$) if ${\gamma}$ = 1 and $Osc_{exp}L^{\gamma}({\mu}){\subset}RBMO({\mu})$ if ${\gamma}$ > 1.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.1
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• pp.43-55
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• 2011

We here investigate the Liouville type theorems of slow diffusion differential inequality and its coupled system with variable coefficients in cone. First, we give the definition of global weak solution, and then we establish the universal estimate (does not depend on the initial value) of solution by constructing test function. At last, we obtain the nonexistence of non-negative non-trivial global weak solution within the appropriate critical exponent. The main feature of this method is that we need not use comparison theorem or the maximum principle.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1029-1036
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• 1997

Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.

• The Bulletin of The Korean Astronomical Society
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• v.38 no.2
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• pp.59.1-59.1
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• 2013

Type Ia supernovae (SNe) are providing the most conclusive evidence for accelerating universe with dark energy in observational cosmology. In these investigations, look-back time evolution of SNe luminosity is regarded as negligible on the basic assumption. However, several recent works present some systematic differences among hosts which have different characteristics of stellar population. For more direct investigation, we are proceeding with our YONSEI (YOnsei Nearby Supernovae Evolution Investigation) project. Only early-type hosts in our catalogue were chosen in order to estimate the luminosity-weighted mean age and metallicity directly using Single Stellar Population (SSP) models and ignore the effect from the dust extinction. Observations using low-resolution spectrographs are still in progress at Las Campanas Observatory with 2.5m telescope and at McDonald Observatory with 2.7m telescope. We have thus far obtained spectra for 30 early-type hosts. After weak emission line correction, Lick/IDS absorption-line indices are measured and YEPS spectroscopic evolution model was applied to determine mean population ages and metallicities. Our preliminary results show that SNe Ia hosted in older galaxies seem to be brighter at 1.4 - 3 sigma levels, however, more observations and analyses are still needed to confirm this correlation.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.74.2-74.2
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• 2019

Mass measurement of high-redshift galaxy clusters with high accuracy is important in constraining cosmological parameters. Extremely massive clusters at high redshift may impose a serious tension with the current ΛCDM paradigm. SPT-CL J2040-4451 at z=1.48 is considered one such case given its redshift and mass estimate inferred from the SZ data. The system has also been confirmed to be indeed massive from a recent weak-lensing (WL) analysis. Comparison of the WL mass with the spectroscopic result may provide invaluable information on the dynamical stage of the system. However, the existing spectroscopic coverage of the cluster is extremely poor; only 6 blue star-forming galaxies have been found within the virial radius, which results in highly inflated and biased velocity dispersion. In this work, we present a spectroscopic analysis of the member candidates using Gemini Multi-Object Spectrographs (GMOS) observation in Gemini South. The observation was designed to find early-type member galaxies within the virial radius and to obtain reliable velocity dispersion. We explain our selection scheme and preliminary results of the spectra. We also compare the dynamical mass estimate inferred from the velocity dispersion with the WL mass.