• Journal of the Korean Mathematical Society
• /
• v.46 no.3
• /
• pp.523-550
• /
• 2009

In the paper two-weight inequalities of various type for strong fractional maximal functions and potentials with multiple kernels defined on $\mathbb{R}^2$ are established.

• Journal of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.57-72
• /
• 2016

We establish maximal moment inequalities of partial sums under ${\psi}$-weak dependence, which has been proposed by Doukhan and Louhichi [P. Doukhan and S. Louhichi, A new weak dependence condition and application to moment inequality, Stochastic Process. Appl. 84 (1999), 313-342], to unify weak dependence such as mixing, association, Gaussian sequences and Bernoulli shifts. As an application of maximal moment inequalities, a functional central limit theorem is developed for linear processes with ${\psi}$-weakly dependent innovations.

• Journal of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.625-633
• /
• 1995

Classical Fatous' theorem asserts that the non-tangential limit of the Poisson integral of an integrals function on $[\pi, \pi]$ exists a.e.

• Journal of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.361-370
• /
• 1998

A condition for a certain maximal operator to be of weak type (p, p) is studied. This operator unifies various maximal operators cited in the literatures.

• Journal of the Korean Mathematical Society
• /
• v.58 no.3
• /
• pp.525-552
• /
• 2021

In this paper, we introduce two general iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of the variational inequality problems for a continuous monotone mapping, the zero point set of a set-valued maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative algorithms to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets.

• Communications of the Korean Mathematical Society
• /
• v.14 no.3
• /
• pp.581-595
• /
• 1999

In the present paper we provide a short of the uni-form CLT for the function-indexed martingale difference process under the uniformly integrable entropy by establishing a maximal inequality.

• Journal of the Korean Mathematical Society
• /
• v.45 no.6
• /
• pp.1561-1576
• /
• 2008

In this paper we shall prove some weighted norm inequalities of the form $${\int}_{R^n}\;|Tf(x)|^pu(x)dx\;{\leq}\;C_p\;{\int}_{R^n}\;|f(x)|^pNu(x)dx$$ for certain rough singular integral T and maximal singular integral $T^*$. Here u is a nonnegative measurable function on $R^n$ and N denotes some maximal operator. As a consequence, some vector valued inequalities for both T and $T^*$ are obtained. We shall also get a boundedness result of T on the Triebel-Lizorkin spaces.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.1
• /
• pp.35-42
• /
• 2012

In this paper we first introduce a Carleson inequality and study the generalized form of Carleson inequality in the context of spaces of homogeneous type. The previous inequality is known to play important roles in harmonic analysis.

• Bulletin of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.279-292
• /
• 1998

We derive maximal inequalities of linearly positive quadrant dependent (LPQD) random variables for d = 1,2. With an application we also obtain the weak convergence for 2-parameter arrays of LPQD random variables.

• Journal of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.163-176
• /
• 2001

We examine Orlicz-type integral inequalities for operators and obtain as a corollary a characterization of such inequalities for the Hardy-Littlewood maximal operator extending the well-known L(sup)p-norm inequalities.