• 대한수학회지
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• 제42권3호
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• pp.405-434
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• 2005

We establish appropriate $L^p$ estimates for a class of maximal operators $S_{\Omega}^{(\gamma)}$ on the product space $R^n\;\times\;R^m\;when\;\Omega$ lacks regularity and $1\;\le\;\gamma\;\le\;2.\;Also,\;when\;\gamma\;=\;2$, we prove the $L^p\;(2\;{\le}\;P\;<\;\infty)\;boundedness\;of\;S_{\Omega}^{(\gamma)}\;whenever\;\Omega$ is a function in a certain block space $B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ (for some q > 1). Moreover, we show that the condition $\Omega\;{\in}\;B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ is nearly optimal in the sense that the operator $S_{\Omega}^{(2)}$ may fail to be bounded on $L^2$ if the condition $\Omega\;{\in}\;B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ is replaced by the weaker conditions $\Omega\;{\in}\;B_q^{(0,\varepsilon)}(S^{n-1}\;\times\;S^{m-1})\;for\;any\;-1\;<\;\varepsilon\;<\;0.$

• 호남수학학술지
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• 제46권2호
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• pp.237-248
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• 2024

In this manuscript, the hypersurfaces of non-flat Riemannian 4-space forms are considered. A hypersurface of a 4-dimensional Riemannian space form defined by an isometric immersion 𝐱 : M³ → 𝕄⁴(c) is said to be biconservative if it satisfies the equation (∆²𝐱 )^⊤ = 0, where ∆ is the Laplace operator on M³ and ⊤ stands for the tangent component of vectors. We study an extended version of biconservativity condition on the hypersurfaces of the Riemannian standard 4-space forms. The C-biconservativity condition is obtained by substituting the Cheng-Yau operator C instead of ∆. We prove that C-biconservative hypersurfaces of Riemannian 4-space forms (with some additional conditions) have constant scalar curvature.

• Korean Journal of Mathematics
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• 제28권1호
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• pp.137-147
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• 2020

In this paper, we introduce two subclasses of analytic and Spiral-like functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes.

• East Asian mathematical journal
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• 제26권3호
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• pp.403-413
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• 2010

In this paper, we consider a doubly nonlinear parabolic equation related to the Leray-Lions operator with Dirichlet boundary condition and initial data given. By exploiting a suitable implicit time-discretization technique, we obtain the existence of global strong solution.

• 대한수학회지
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• 제35권1호
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• pp.11-21
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• 1998

A condition for a certain maximal operator to be of strong type (p,p) is characterized in terms of Carleson measure.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.105-115
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• 2021

Generalized pseudo-differential operators (PDO) involving fractional Fourier transform associate with the symbol a(x, y) whose derivatives satisfy certain growth condition is defined. The product of two generalized pseudo-differential operators is shown to be a generalized pseudo-differential operator.

• Korean Journal of Acupuncture
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• 제21권4호
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• pp.1-19
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• 2004

Objectives : To understanding biological mechanism of acupuncture therapy, we have proposed a hypothesis. First of all, there exists electric property in meridian and meridian point. Second of all, energy flowing in meridian is related with electric property. Third of all, there is electronic interaction between the operator who performs acupuncture therapy and the receiver who is given acupuncture therapy. Forth of all, acupuncture effects may depend on the electric capacity which is transferred between the operator and the receiver via acupuncture needle. Methods : Under the hypothesis, we studied the effects of electric change in $ST_{37}(+)\;and\;ST_{39}(-)$ generated by Tanchim (彈鍼) manipulation which was stimulated at $ST_{36}$ point. And compared with data on the changes of electric change from the hand of the operator during acupuncture stimulation. Electric charge induced via acupuncture needle from the operator may be important factor that causes the changes of electric change in meridian and acupoint in the receiver. Therefore we investigated the changes of electric charge induced by the operator using Maclab 400 by the following methods. The one was in stable electric circle condition and the other was in unstable electric circle condition. Results : In this experiments, the changes of electric change from the stimulation type of Tanchim manipulation performed in our lab condition in acupuncture therapy was induced at least three factor, one was the difference of bio-potentials between the operator and the receiver of acupuncture therapy, another was the depth of acupuncture insertion from the skin of the receiver, the other was an electromyogram of the receiver. Conclusion : The data imply that the first factor should make a capacitance current when the operator touched the acupuncture needle which was inserted in the receiver. Therefore, the results suggest that capacitance currents stimulus in electronic view may be important factor in acupuncture therapy between the operator and the receiver of acupuncture therapy.

• Korean Journal of Acupuncture
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• 제22권4호
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• pp.9-27
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• 2005

Objective : hypothesis. First of all, there exists electric property in meridian and meridian point. Second of all, energy flowing in meridian is related with electric property. Third of all, there is electronic interaction between the operator who performs acupuncture therapy and the receiver who is given acupuncture therapy. Forth of all, acupuncture effects may depend on the electric capacity which is transferred between the operator and the receiver via acupuncture needle. Methods : Under the hypothesis, I studied the effects of electric charge in ST37(+) and ST39(-) generated by Apchim (押鍼) manipulation which was stimulated at ST36 point. And compared with data on the changes of electric charge from the hand of the operator during acupuncture stimulation. Electric charge induced via acupuncture needle from the operator may be important factor that causes the changes of electric charge in meridian and acupoint in the receiver. Therefore we investigated the changes of electric charge induced by the operator using Maclab 400 by the following methods. The one was in stable electric circle condition and the other was in unstable electric circle condition. In this experiments, the changes of electric charge from the stimulation type of Apchim manipulation performed in our lab condition in acupuncture therapy was induced at least three factor, one was the difference of bio-potentials between the operator and the receiver of acupuncture therapy, another was the depth of acupuncture insertion from the skin of the receiver the other was an electromyogram of the receiver. Results :The data imply that the first factor should make a capacitance current when the operator touched the acupuncture needle which was inserted in the receiver. Therefore, the results suggest that capacitance currents stimulus in electronic view may be important factor in acupuncture therapy between the operator and the receiver of acupuncture therapy.

• 대한수학회보
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• 제47권4호
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• pp.743-750
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• 2010

For several Banach spaces X and Y and operator ideal $\cal{U}$, if $\cal{U}$(X, Y) denotes the component of operator ideal $\cal{U}$; according to Freedman's definitions, it is shown that a necessary and sufficient condition for a closed subspace $\cal{M}$ of $\cal{U}$(X, Y) to have the alternative Dunford-Pettis property is that all evaluation operators $\phi_x\;:\;\cal{M}\;{\rightarrow}\;Y$ and $\psi_{y^*}\;:\;\cal{M}\;{\rightarrow}\;X^*$ are DP1 operators, where $\phi_x(T)\;=\;Tx$ and $\psi_{y^*}(T)\;=\;T^*y^*$ for $x\;{\in}\;X$, $y^*\;{\in}\;Y^*$ and $T\;{\in}\;\cal{M}$.

• Kyungpook Mathematical Journal
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• 제51권1호
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• pp.77-85
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• 2011

In this paper, we introduce the integral operator $I_{\beta}$($p_1$, ${\ldots}$, $p_n$; ${\alpha}_1$, ${\ldots}$, ${\alpha}_n$)(z) analytic functions with positive real part. The radius of convexity of this integral operator when ${\beta}$ = 1 is determined. In particular, we get the radius of starlikeness and convexity of the analytic functions with Re {f(z)/z} > 0 and Re {f'(z)} > 0. Furthermore, we derive sufficient condition for the integral operator $I_{\beta}$($p_1$, ${\ldots}$, $p_n$; ${\alpha}_1$, ${\ldots}$, ${\alpha}_n$)(z) to be analytic and univalent in the open unit disc, which leads to univalency of the operators $\int\limits_0^z(f(t)/t)^{\alpha}$dt and $\int\limits_0^z(f'(t))^{\alpha}dt$.