• 대한수학회보
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• 제44권4호
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• pp.701-708
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• 2007

In this paper we characterize the boundedness, compactness and closedness of the range of the weighted composition operators on Lorentz spaces L(p,q), $1.

• Kyungpook Mathematical Journal
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• 제48권3호
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• pp.387-393
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• 2008

In this note, we present some inequalities for the norm and numerical radius of 2-homogeneous polynomials from the 2-dimensional real space $l_p^2$, (1 < p < $\infty$) to itself in terms of their coefficients. We also give an upper bound for n^{(k)}(l_p^2), (k = 2, 3, $\cdots$).

• East Asian mathematical journal
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• 제19권1호
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• pp.73-80
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• 2003

Let D be a bounded domain in $\mathbb{C}^n$ with $C^2$ boundary. In this paper, we prove the following inequality $${\parallel}u{\parallel}_{p_2,{\alpha}_2}{\lesssim}{\parallel}u{\parallel}_{p_1,{\alpha}_1}+{\parallel}\bar{\partial}u{\parallel}_{p_1,{\alpha}_1+p_1}/2$$, where $1{\leq}p_1{\leq}p_2<\infty,\;{\alpha}_j>0,(n+{\alpha}_1)/p_1=(n+{\alpha}_1)/p_1=(n+{\alpha}_2)/p_2$, and $1/p_2{\geq}1/p_1-1/2n$.

• 대한수학회지
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• 제46권3호
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• pp.577-588
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• 2009

In this paper, the author studies the k-th commutators of oscillatory singular integral operators with a BMO function and phases more general than polynomials. For 1 < p < $\infty$, the $L^p$-boundedness of such operators are obtained provided their kernels belong to the spaces $L(log+L)^{k+1}(S^{n-1})$. The results of the corresponding maximal operators are also established.

• 대한수학회지
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• 제44권3호
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• pp.733-745
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• 2007

We prove the $L^p(1 boundedness of the parabolic Marcinkiewicz integral with the kernel function $\Omega{\in}L(log^+L)^{1/2}(S^{n-1})$. The result is an improvement and extension of some known results.

• 대한수학회지
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• 제44권6호
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• pp.1417-1428
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• 2007

We obtain weighted $L^p$ estimates $(1{\leq}p<{\infty})\;for\;\bar{\partial}$ on convex domains with piecewise smooth boundaries in $\mathbb{C}^2$ by using explicit formulas of solutions introduced by Berndtsson and Andersson.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.537-545
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• 2007

We investigate complemented Banach sublattices of the Banach envelope of $Weak_L1$. In particular, the Banach envelope of $Weak_L1$ contains a complemented Banach sublattice that is isometrically isomorphic to a nonseparable Banach lattice $l_p(S),\;1{\leq}p<{\infty}\;and\;|S|{\leq}2^{{\aleph}0}$.

• 충청수학회지
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• 제23권2호
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• pp.271-277
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• 2010

We prove the global (in time) vorticity existence for the 2-D Euler equations of a perfect incompressible fluid in $B^0_{{\infty},1}({\mathbb{R}}^2){\cap}L^p({\mathbb{R}}^2)$ with 1 < p < 2. Moreover, we prove that the particle trajectory map X(x, t) satisfies the following estimate: for some positive constant C $${\parallel}X^{\pm1}(\cdot,\;t)-id(\cdot){\parallel}_{B^1_{\infty,1}}{\leq}Ce^{e^{Ct}}$$, where id represents the identity map on ${\mathbb{R}}^2$.

• 대한수학회논문집
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• 제28권2호
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• pp.231-241
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• 2013

On the framework of the 2-adic group $\mathcal{Z}_2$, we study a Sobolev-like inequality where we estimate the $L^2$ norm by a geometric mean of the BV norm and the $\dot{B}_{\infty}^{-1,{\infty}}$ norm. We first show, using the special topological properties of the $p$-adic groups, that the set of functions of bounded variations BV can be identified to the Besov space ˙$\dot{B}_1^{1,{\infty}}$. This identification lead us to the construction of a counterexample to the improved Sobolev inequality.

• International Journal of Reliability and Applications
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• 제8권2호
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• pp.137-151
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• 2007

Posbist reliability of typical systems is preliminarily discussed in Cai (1991). In this paper, we focus on the posbist reliability analysis of some typical systems in depth. First, the lifetime of the system is dealt as a fuzzy variable defined on the possibility space (U, ${\phi}$, $P_{oss}$) and the universe of discourse is expanded from (0, $+{\infty}$) to ($-{\infty},\;+{\infty}$). Then, a concrete possibility distribution function of the fuzzy variable is given, i.e., a Gaussian fuzzy variable. Finally, posbist reliability of typical systems (series, parallel, series-parallel, parallel-series, cold redundant system) is deduced. The expansion makes the proofs of some theorems straightforward and allows us to easily obtain the posbist reliability of typical systems. To illustrate the method a numerical example is given.