• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.977-991
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• 2008

We characterize the boundedness and compactness of the weighted composition operator $uC_{\psi}$ from the general function space F(p, q, s) into the logarithmic Bloch space ${\beta}_L$ on the unit disk. Some necessary and sufficient conditions are given for which $uC_{\psi}$ is a bounded or a compact operator from F(p,q,s), $F_0$(p,q,s) into ${\beta}_L$, ${\beta}_L^0$ respectively.

• East Asian mathematical journal
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• v.30 no.1
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• pp.63-67
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• 2014

Observing that for any P'-space X, ${\Lambda}vX$ is a P'-space if vX is a weakly Lindel$\ddot{o}$f space, (${\Lambda}vX{\times}{\Lambda}Y$, ${\Lambda}_X{\times}{\Lambda}_Y$) is the minimal basically disconnected cover of $X{\times}Y$ for a countably locally weakly Lindel$\ddot{o}$f space Y.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.316-324
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• 2023

The P-curvature tensor has been studied in the space-time of general relativity and it is found that the contracted part of this tensor vanishes in the Einstein space. It is shown that Rainich conditions for the existence of non-null electro variance can be obtained by P_𝛼𝛽. It is established that the divergence of tensor G_𝛼𝛽 defined with the help of P_𝛼𝛽 and scalar P is zero, so that it can be used to represent Einstein field equations. It is shown that for V₄ satisfying Einstein like field equations, the tensor P_𝛼𝛽 is conserved, if the energy momentum tensor is Codazzi type. The space-time satisfying Einstein's field equations with vanishing of P-curvature tensor have been considered and existence of Killing, conformal Killing vector fields and perfect fluid space-time has been established.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.91-95
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• 1984

Let D$^{p}$ be the space of distributions of $L^{p}$-growth and S the space of tempered destributions in $R^{n}$: D$^{p}$, 1.leq.P.leq..inf., is the dual of the space $D^{p}$ which we discribe later. We denote by O$_{c}$(S:S') the space of convolution operators in S. In [8] S. Sznajder and Z. Zielezny proved the following necessary conditions for convolution operators in O$_{c}$(S:S) to be solvable in S.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.1043-1052
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• 2011

We introduce a new norm, called the $N^p$-norm (1 $\leq$ p < ${\infty}$ on the space $N^p$(V,W) where V and W are abstract operator spaces. By proving some fundamental properties of the space $N^p$(V,W), we also discover that if W is complete, then the space $N^p$(V,W) is also a Banach space with respect to this norm for 1 $\leq$ p < ${\infty}$.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.315-330
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• 1998

Chen and Piccinni [7] have classified all compact surfaces in a Euclidean space $R^{2＋p}$ with 1-type generalized Gauss map. Being motivated by this result, the purpose of this paper is to consider the Lorentz version of the classification theorem and to obtain a complete classification of space-like surfaces in indefinite Euclidean space $R_{p}$ $^{2＋p}$ with 1-type generalized Gauss map.p.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.171-181
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• 1999

In this note, we will prove that the operator-valued function space integral as an operator from $L_p\;to\;L_{p'}$ (1

• Communications of the Korean Mathematical Society
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• v.24 no.4
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• pp.561-564
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• 2009

A holomorphic function space in the unit disc D satisfying $\int_D|f'(z)|^p(1-|z|^2)^{p-1}dA(z)$<$\infty$ is quite close to $H^p$. The problems on the existence of the radial limits are considered for this space. It is proved that the situation for p > 2 is totally different from the situation for p $\leq$ 2.

• The Korean Journal of Pain
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• v.19 no.2
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• pp.168-174
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• 2006

Background: Several biochemical mediators, such as substance P, calcitonin gene-related peptide (CGRP) and prostaglandin $E_2$, have been demonstrated to be involved in herniated or degenerated disc-induced radiculopathy. The authors tested the hypothesis that these mediators would existed in the epidural space of humans. Methods: Thirty nine patients were divided into two groups; 27 patients, who were diagnosed with spinal stenosis (stenosis group), and 12 scheduled for epidural anesthesia, without a history of back pain (control group). Under fluoroscopic guidance, an epidural catheter was introduced through the caudal space and placed into the anterior and posterior spaces, up to and around the epidural adhesive area, in the stenosis group. In the control group, the catheter was placed into the posterior epidural space through the L3⁣-4 or L4⁣-5 intervertebral space. Epidural irrigation was performed with 10 ml of saline, via an epidural catheter. Aspirated lavage fluid was collected, and the concentrations of biochemical mediators (substance P, CGRP and prostaglandin $E_2$) measured using an enzyme immunoassay kit. Results: Substance P, CGRP and prostaglandin $E_2$ were detected in all the epidural lavage fluids from both groups. The concentrations of substance P and prostaglandin $E_2$ in the stenosis group were higher than those of the control (P < 0.05). However, there was no difference in the CGRP levels between the two groups. In the stenosis group, the concentrations of these three mediators in the anterior epidural space were no different to those in the posterior space. Conclusions: These results suggest that biochemical mediators, such as substance P and prostaglandin $E_2$, in the epidural space might be partly involved in pain mechanism associated with spinal stenosis.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1159-1170
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• 2020

We consider the weighted spaces ℓ^p(𝕊, 𝜑) and ℓ^p(𝕊, 𝜓) for 1 < p < +∞, where 𝜑 and 𝜓 are weights on 𝕊 (= ℕ or ℤ). We obtain a sufficient condition for ℓ^p(𝕊, 𝜓) to be multiplier weighted-space of ℓ^p(𝕊, 𝜑) and ℓ^p(𝕊, 𝜓). Our condition characterizes the last multiplier weighted-space in the case where 𝕊 = ℤ. As a consequence, in the particular case where 𝜓 = 𝜑, the weighted space ℓ^p(ℤ,𝜓) is a convolutive algebra.