• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.425-437
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• 2002

Let $\Omega$ be a smoothly bounded pseudoconvex domain in $C^{n}$ and let $z^{0}$ $\in$b$\Omega$ a point of finite type. We also assume that the Levi form of b$\Omega$ is comparable in a neighborhood of $z^{0}$ . Then we get precise estimates of the Bergman kernel function, $K_{\Omega}$(z, w), and its derivatives in a neighborhood of $z^{0}$ . .

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.65-74
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• 2006

In this paper, we will define the Bergman projection type operator Pr and find conditions on which the operator Pr is bound-ed on $L^p$(B, dv). By using the properties of the Bergman projection type operator Pr, we will show that if $f{\in}L_a^p$(B, dv), then $(1-{\parallel}{\omega}{\parallel}^2){\nabla}f(\omega){\cdot}z{\in}L^p(B,dv)$. We will also show that if $(1-{\parallel}{\omega}{\parallel}^2)\; \frac{{\nabla}f(\omega){\cdot}z}{},\;{\in}L^p{B,\;dv),\;then\;f{\in}L_a^p(B,\;dv)$.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.713-732
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• 2017

Let ${\Omega}{\in}L^s(S^{n-1})$ for s > 1 be a homogeneous function of degree zero and b be BMO functions or Lipschitz functions. In this paper, we obtain some boundedness of the $Calder{\acute{o}}n$-Zygmund singular integral operator $T_{\Omega}$ and its commutator [b, $T_{\Omega}$] on Herz-type Hardy spaces with variable exponent.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.399-411
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• 1996

Let $\Omega$ be a smoothly bounded pseudoconvex domain in $C^n$ and let $A(\Omega)$ denote the functions holomorphic on $\Omega$ and continuous on $\bar{\Omega}$. A point $p \in b\Omega$ is a peak point if there is a function $f \in A(\Omega)$ such that $f(p) = 1, and $\mid$f(z)$\mid$ < 1 for z \in \bar{\Omega} - {p}$.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.545-565
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• 2016

In this paper, we present some general results on the pointwise convergence of the non-convolution type nonlinear singular integral operators in the following form: $$T_{\lambda}(f;x)={\large\int_{\Omega}}K_{\lambda}(t,x,f(t))dt,\;x{\in}{\Psi},\;{\lambda}{\in}{\Lambda}$$, where ${\Psi}$ = and ${\Omega}$ = stand for arbitrary closed, semi-closed or open bounded intervals in ${\mathbb{R}}$ or these set notations denote $\mathbb{R}$, and ${\Lambda}$ is a set of non-negative numbers, to the function $f{\in}L_{p,{\omega}}({\Omega})$, where $L_{p,{\omega}}({\Omega})$ denotes the space of all measurable functions f for which $\|{\frac{f}{\omega}}\|^p$ (1 ${\leq}$ p < ${\infty}$) is integrable on ${\Omega}$, and ${\omega}:{\mathbb{R}}{\rightarrow}\mathbb{R}^+$ is a weight function satisfying some conditions.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.399-412
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• 2001

In this paper, we consider that the q-analogue of w$\omega-Bernoulli numbers\; B_i(\omega, q)$. And we calculate the sums of products of two q-analogue of $\omega-Bernoulli numbers B_i(\omega, q)$ in complex cases. From this result, we obtain the Euler type formulas of the Carlitz´s q-Bernoulli numbers $\beta_i(q)$ and q-Bernoulli numbers $B_i(q)$. And we also calculate the p-adic Stirling type series by the definition of $B_i(\omega, q)$ in p-adic cases.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.87-101
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• 2018

The purpose of this paper is to define a new class of hyperholomorphic functions spaces, which will be called $F^{\alpha}_{{\omega},G}$(p, q, s) type spaces. For this class, we characterize hyperholomorphic weighted ${\alpha}$-Bloch functions by functions belonging to $F^{\alpha}_{{\omega},G}$(p, q, s) spaces under some mild conditions. Moreover, we give some essential properties for the extended weighted little ${\alpha}$-Bloch spaces. Also, we give the characterization for the hyperholomorphic weighted Bloch space by the integral norms of $F^{\alpha}_{{\omega},G}$(p, q, s) spaces of hyperholomorphic functions. Finally, we will give the relation between the hyperholomorphic ${\mathcal{B}}^{\alpha}_{{\omega},0}$ type spaces and the hyperholomorphic valued-functions space $F^{\alpha}_{{\omega},G}$(p, q, s).

• Journal of Aquaculture
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• v.10 no.2
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• pp.219-225
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• 1997

The growth and size variation of rotifer (Brachionus plicatils) were examined at the various water temepratures ranging form 18 to $36^{\circ}C$, and under continuous light condition. Either Chlorella ellipsoidea or $\omega$-yeast were fed to rotifer as a food organism. Compared to large-type rotifer fed of $\omega$-yeast, those fed on C. ellipsoildea generally showed higher growth at 7th after starting culture under the water temperaure of less than $30^{\circ}C$. Above such temperature, the large-type rotifer fed on $\omega$-yeast showed higher growth rather than those fed on C. ellipsoidea and the maximum cell number reached 1,420 ind./m$\ell$ at $36^{\circ}C$, whereas when the small-type rotifer was fed on $\omega$-teast, its maximum cell number was to be 1,669 ind./m$\ell$at $34^{\circ}C$. The striking decrease in size was found in large-type rotifer which was to be $112.1\mu m$m(initial : 202.0${\mu}{\textrm}{m}$) when they were fed on C. ellipsoidea at $34^{\circ}C$ for 5 days after starting culture. A great increase in size from the initial of 157.0 to $201.3\mu m$mwas show in small-type rotifer fed on $\omega$-yeast at $20^{\circ}C$,for 5 days. The present results demonstrated that size variation of rotifer could be controlled by changing culture temperature.

• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.65-74
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• 2007

Suppose that $\mu$ is a finite positive Borel measure on bounded symmetric domain $\Omega{\subset}\mathbb{C}^n\;and\;\nu$ is the Euclidean volume measure such that $\nu(\Omega)=1$. Suppose 1 < p < $\infty$ and r > 0. In this paper, we will show that the norms $sup\{\int_\Omega{\mid}k_z(w)\mid^2d\mu(w)\;:\;z\in\Omega\}$, $sup\{\int_\Omega{\mid}h(w)\mid^pd\mu(w)/\int_\Omega{\mid}h(w)^pd\nu(w)\;:\;h{\in}L_a^p(\Omega,d\nu),\;h\neq0\}$ and $$sup\{\frac{\mu(E(z,r))}{\nu(E(z,r))}\;:\;z\in\Omega\}$$ are are all equivalent. We will also show that the inclusion mapping $ip\;:\;L_a^p(\Omega,d\nu){\rightarrow}L^p(\Omega,d\mu)$ is compact if and only if lim $w\rightarrow\partial\Omega\frac{\mu(E(w,r))}{\nu(E(w,r))}=0$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1741-1751
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• 2016

We prove the boundary Harnack principle and the Carleson type estimate for ratios of solutions u/v of non-divergence second order elliptic equations $Lu=a_{ij}D_{ij}+b_iD_iu=0$ in a bounded domain ${\Omega}{\subset}R_n$. We assume that $b_i{\in}L^n({\Omega})$ and ${\Omega}$ is a $H{\ddot{o}}lder$ domain of order ${\alpha}{\in}$ (0, 1) satisfying a strong regularity condition.