• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1915-1922
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• 2013

We prove the admissibility of the space $L_0(\mathcal{A},X)$ of vector-valued measurable functions determined by real-valued finitely additive set functions defined on algebras of sets.

• East Asian mathematical journal
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• v.21 no.1
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• pp.41-48
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• 2005

In this paper we first introduce a space of homogeneous type X, and then consider a kind of generalized upper half-space $X{\times}(0,\;\infty)$. We are mainly considered with inequalities for the $L^p$ norms of area functions associated with approach regions in $X{\times}(0,\;\infty)$.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.393-402
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• 2013

For 0 < $p$ < ${\infty}$, ${\alpha}$ > -1 and 0 < $r$ < 1, we show that if $f$ is in the space of Dirichlet type $\mathfrak{D}^p_{p-1}$, then ${\int}_{1}^{0}M_{p}^{p}(r,f^{\prime})(1-r)^{p-1}rdr$ < ${\infty}$ and ${\int}_{1}^{0}M_{(2+{\alpha})p}^{(2+{\alpha})p}(r,f^{\prime})(1-r)^{(2+{\alpha})p+{\alpha}}rdr$ < ${\infty}$ where $M_p(r,f)=\[\frac{1}{2{\pi}}{\int}_{0}^{2{\pi}}{\mid}f(re^{it}){\mid}^pdt\]^{1/p}$. For 1 < $p$ < $q$ < ${\infty}$ and ${\alpha}+1$ < $p$, we show that if there exists some positive constant $c$ such that ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathfrak{D}^p_{\alpha}}$ for all $f{\in}\mathfrak{D}^p_{\alpha}$, then ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathcal{B}_p(q)}$ where $\mathcal{B}_p(q)$ is the weighted Besov space. We also find the condition of measure ${\mu}$ such that ${\sup}_{a{\in}D}{\int}_D(k_a(z)(1-{\mid}a{\mid}^2)^{(p-a-1)})^{q/p}d{\mu}(z)$ < ${\infty}$.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.469-477
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• 2024

For a knot in the 3-sphere, the Upsilon invariant is a piecewise linear function defined on the interval [0, 2]. It is known that this invariant of an L-space knot is the Legendre-Fenchel transform (or, convex conjugate) of a certain gap function derived from the Alexander polynomial. To recover an information lost in the Upsilon invariant, Kim and Livingston introduced the secondary Upsilon invariant. In this note, we prove that the secondary Upsilon invariant of an L-space knot is a concave conjugate of a restricted gap function. Also, a similar argument gives an alternative proof of the above fact that the Upsilon invariant of an L-space knot is a convex conjugate of a gap function.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.93-111
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• 2004

In this paper, we use a generalized Brownian motion process to define a generalized Feynman integral and a generalized Fourier-Feynman transform. We also define the concepts of the multiple Lp analytic generalized Fourier-Feynman transform and the generalized convolution product of functional on function space $C_{a,\;b}[0,\;T]$. We then verify the existence of the multiple $L_{p}$ analytic generalized Fourier-Feynman transform for functional on function space that belong to a Banach algebra $S({L_{a,\;b}}^{2}[0, T])$. Finally we establish some relationships between the multiple $L_{p}$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $S({L_{a,\;b}}^{2}[0, T])$.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.86-86
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• 2019

We present BV photometric observations and high-resolution spectra of AO Ser, which were obtained at the Mt. Lemmon Optical Astronomy Observatory (LOAO) and the Bohyunsan Optical Astronomy Observatory (BOAO), respectively, in 2017. The radial velocities (RVs) for both components were measured, and the effective temperature of the primary star was found to be $T_{eff,1}=8,820{\pm}62K$ by a comparison of the observed spectra and the Kurucz models. A unique set of fundamental parameters of AO Ser were derived for the first time by a simultaneous analysis of the light and RV curves. The results indicate that our program target is a semi-detached eclipsing system with values of $M_1=2.06{\pm}0.11M_{\odot}$ and $M_2=0.41{\pm}0.03M_{\odot}$, $R_1=1.54{\pm}0.03R_{\odot}$ and $R_2=1.30{\pm}0.02R_{\odot}$, and $L_1=12.9{\pm}0.2L_{\odot}$ and $L_2=0.9{\pm}0.3L_{\odot}$. We applied multiple frequency analyses to the eclipse-subtracted light residuals. As a result, two frequencies of $f_1=21.85151days^{-1}$ and $f_2=23.48405days^{-1}$ were detected and their pulsation constants were calculated to $Q_1=0.0344days$ and $Q_2=0.0320days$. The pulsational characteristics and the position in the HR diagram demonstrate that the primary star is a ${\delta}$ Sct pulsator.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.483-492
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• 2007

In this paper, we study the map projections from pseudo-sphere $S_1^2$ onto the non-lightlike surfaces in the 3-dimensional Lorentzian space, $L^3$, with curvature zero. We show geometrical means and properties of $\mathbb{R}{\times}S_1^1-cylindrical$, $S^1{\times}L-cylindrical$ and $\mathbb{R}{\times}H_0^1-cylindrical$ projections defined on $S_1^2$ to cylinders $\mathbb{R}{\times}S_1^1,\;S^1{\times}L$ and $\mathbb{R}{\times}H_0^1$, respectively, and orthographic and stereographic projections on $S_1^2$ to Lorentzian plane, $L^2$.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.781-791
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• 2016

Let $d_*(1,w)^2 ={\mathbb{R}}^2$ with the octagonal norm of weight w. It is the two dimensional real predual of Lorentz sequence space. In this paper we classify the smooth points of the unit ball of the space of symmetric bilinear forms on $d_*(1,w)^2$. We also show that the unit sphere of the space of symmetric bilinear forms on $d_*(1,w)^2$ is the disjoint union of the sets of smooth points, extreme points and the set A as follows: $$S_{{\mathcal{L}}_s(^2d_*(1,w)^2)}=smB_{{\mathcal{L}}_s(^2d_*(1,w)^2)}{\bigcup}extB_{{\mathcal{L}}_s(^2d_*(1,w)^2)}{\bigcup}A$$, where the set A consists of $ax_1x_2+by_1y_2+c(x_1y_2+x_2y_1)$ with (a = b = 0, $c={\pm}{\frac{1}{1+w^2}}$), ($a{\neq}b$, $ab{\geq}0$, c = 0), (a = b, 0 < ac, 0 < ${\mid}c{\mid}$ < ${\mid}a{\mid}$), ($a{\neq}{\mid}c{\mid}$, a = -b, 0 < ac, 0 < ${\mid}c{\mid}$), ($a={\frac{1-w}{1+w}}$, b = 0, $c={\frac{1}{1+w}}$), ($a={\frac{1+w+w(w^2-3)c}{1+w^2}}$, $b={\frac{w-1+(1-3w^2)c}{w(1+w^2)}}$, ${\frac{1}{2+2w}}$ < c < ${\frac{1}{(1+w)^2(1-w)}}$, $c{\neq}{\frac{1}{1+2w-w^2}}$), ($a={\frac{1+w(1+w)c}{1+w}}$, $b={\frac{-1+(1+w)c}{w(1+w)}}$, 0 < c < $\frac{1}{2+2w}$) or ($a={\frac{1=w(1+w)c}{1+w}}$, $b={\frac{1-(1+w)c}{1+w}}$, $\frac{1}{1+w}$ < c < $\frac{1}{(1+w)^2(1-w)}$).

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1117-1127
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• 2019

Let ${\mathcal{L}}_2=(-{\Delta})^2+V^2$ be the $Schr{\ddot{o}}dinger$ type operator, where nonnegative potential V belongs to the reverse $H{\ddot{o}}lder$ class $RH_s$, s > n/2. In this paper, we consider the operator $T_{{\alpha},{\beta}}=V^{2{\alpha}}{\mathcal{L}}^{-{\beta}}_2$ and its conjugate $T^*_{{\alpha},{\beta}}$, where $0<{\alpha}{\leq}{\beta}{\leq}1$. We establish the $(L^p,\;L^q)$-boundedness of operator $T_{{\alpha},{\beta}}$ and $T^*_{{\alpha},{\beta}}$, respectively, we also show that $T_{{\alpha},{\beta}}$ is bounded from Hardy type space $H^1_{L_2}({\mathbb{R}}^n)$ into $L^{p_2}({\mathbb{R}}^n)$ and $T^*_{{\alpha},{\beta}}$ is bounded from $L^{p_1}({\mathbb{R}}^n)$ into BMO type space $BMO_{{\mathcal{L}}1}({\mathbb{R}}^n)$, where $p_1={\frac{n}{4({\beta}-{\alpha})}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})}}$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1241-1257
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• 2014

We consider a class of hypoelliptic operators of the following type $$L=\sum_{i,j=1}^{p_0}a_{ij}{\partial}^2_{x_ix_j}+\sum_{i,j=1}^{N}b_{ij}x_i{\partial}_{x_j}-{\partial}_t$$, where ($a_{ij}$), ($b_{ij}$) are constant matrices and ($a_{ij}$) is symmetric positive definite on $\mathbb{R}^{p_0}$ ($p_0{\leqslant}N$). By establishing global Morrey estimates of singular integral on the homogenous space and the relation between Morrey space and weak Morrey space, we obtain the global weak Morrey estimates of the operator L on the whole space $\mathbb{R}^{N+1}$.