• 충청수학회지
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• 제31권1호
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• pp.43-46
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• 2018

It is concerned with the continuity of the Hardy-Little wood maximal function between the classical Lebesgue spaces or the Orlicz spaces. A new approach to the continuity of the Hardy-Littlewood maximal function is presented through the observation that the continuity is closely related to the existence of solutions for a certain type of first order ordinary differential equations. It is applied to verify the continuity of the Hardy-Littlewood maximal function from $L^p({\mathbb{R}}^n)$ to $L^q({\mathbb{R}}^n)$ for 1 ${\leq}$ q < p < ${\infty}$.

• 대한수학회논문집
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• 제18권3호
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• pp.551-558
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• 2003

In this paper we Obtain the Hajeck-Renyi type inequality for the asymptotically almost negatively associated(AANA) random variables and extend some results for negatively associated random variables to the AANA case by applying this inequality.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 추계 학술발표회 논문집
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• pp.209-213
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• 2002

We study maximal second moment inequality and derive complete convergence for weighted sums of asymptotically almost negatively associated(AANA) random variables by applying this inequality. 2000 Mathematics Subject Classification : 60F05

• 대한수학회지
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• 제44권6호
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• pp.1233-1241
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• 2007

We derive a kind of weighted norm inequalities which relate the commutators of potential type operators to the corresponding maximal operators.

• East Asian mathematical journal
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• 제25권2호
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• pp.141-146
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• 2009

In this paper, we introduce a new generalized nonlinear quasivariational inequality and establish its equivalence with a xed point problem by using the resolvent operator technique. Utilizing this equivalence, we suggest two iterative schemes, prove two existence theorems of solutions for the generalized nonlinear quasivariational inequality involving generalized cocoercive mapping and establish some convergence results of the sequences generated by the algorithms. Our results include several previously known results as special cases.

• East Asian mathematical journal
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• 제13권2호
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• pp.149-157
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• 1997

• 대한수학회논문집
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• 제10권1호
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• pp.155-162
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• 1995

Let $\mu$ be a positive Borel measure on $R^n$ which is positive on cubes. For any cube $Q \subset R^n$, a Borel measurable nonnegative function $\varphi_Q$, supported and positive a.e. with respect to $\mu$ in Q, is given. We consider a maximal function $$ M_{\mu}f(x) = sup \int \varphi Q$\mid$f$\mid$d_{\mu} $$ where the supremum is taken over all $\varphi Q$ such that $x \in Q$.

• 대한수학회지
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• 제47권1호
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• pp.71-81
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• 2010

We characterize linear operators that preserve sets of matrix ordered pairs which satisfy extreme cases with respect to maximal column rank inequalities of matrix multiplications over semirings.

• 대한수학회지
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• 제35권3호
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• pp.713-725
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• 1998

Let X and Y be Ito processes with dX$_{s}$ = $\phi$$_{s}$dB$_{s}$ ＋ $\psi$$_{s}$ds and dY$_{s}$ = (equation omitted)dB$_{s}$ ＋ ξ$_{s}$ds. Burkholder obtained a sharp bound on the distribution of the maximal function of Y under the assumption that │Y$_{0}$│$\leq$│X$_{0}$│,│ζ│$\leq$│$\phi$│, │ξ│$\leq$│$\psi$│ and that X is a nonnegative local submartingale. In this paper we consider a wider class of Ito processes, replace the assumption │ξ│$\leq$│$\psi$│ by a more general one │ξ│$\leq$$\alpha$ │$\psi$│ , where a $\geq$ 0 is a constant, and get a weak-type inequality between X and the maximal function of Y. This inequality, being sharp for all a $\geq$ 0, extends the work by Burkholder.der.urkholder.der.

• 대한수학회논문집
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• 제21권2호
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• pp.273-285
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• 2006

In this paper, we shall give an affirmative answer to the question raised by Kim and Tan [1] dealing with generalized vector quasi-variational inequalities which generalize many existence results on (VVI) and (GVQVI) in the literature. Using the maximal element theorem, we derive two theorems on the existence of weak solutions of (GVQVI), one theorem on the existence of strong solution of (GVQVI), and one theorem on strong solution in the 1-dimensional case.