• Kyungpook Mathematical Journal
• /
• v.47 no.2
• /
• pp.253-265
• /
• 2007

In this paper, the boundedness for some multilinear operators generated by singular integralv operators and Lipschitz functions on Hardy and Herz-type spaces are obtained.

• Communications of the Korean Mathematical Society
• /
• v.19 no.3
• /
• pp.435-452
• /
• 2004

In this paper, we prove the weighted continuity of multilinear Marcinkiewicz operators for the extreme cases of p.

• Journal of the Korean Mathematical Society
• /
• v.44 no.3
• /
• pp.541-564
• /
• 2007

In this paper, the endpoint estimates for some multilinear operators related to certain integral operators are obtained. The operators include Littlewood-Paley operators and Marcinkiewicz operators.

• Communications of the Korean Mathematical Society
• /
• v.22 no.2
• /
• pp.259-275
• /
• 2007

The continuity for the multilinear operators associated to some non-convolution type integral operators on Besov spaces are obtained. The operators include Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.207-216
• /
• 2024

This note is devoted to establishing the variation continuity of the one-dimensional discrete uncentered multilinear maximal operator. The above result is based on some refine variation estimates of the above maximal functions on monotone intervals. The main result essentially improves some known ones.

• Smart Media Journal
• /
• v.7 no.4
• /
• pp.90-98
• /
• 2018

A Multilinear LDA Method of Tensor Representation for ECG Signal Based Individual Identification Electrocardiogram signals, included in the cardiac electrical activity, are often analyzed and used for various purposes such as heart rate measurement, heartbeat rhythm test, heart abnormality diagnosis, emotion recognition and biometrics. The objective of this paper is to perform individual identification operation based on Multilinear Linear Discriminant Analysis (MLDA) with the tensor feature. The MLDA can solve dimensional aspects of classification problems in high-dimensional tensor, and correlated subspaces can be used to distinguish between different classes. In order to evaluate the performance, we used MPhysionet's MIT-BIH database. The experimental results on this database showed that the individual identification by MLDA outperformed that by PCA and LDA.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.6
• /
• pp.1427-1449
• /
• 2020

In this paper, we establish the boundedness of the m-linear Calderón-Zygmund operators on product of central Morrey spaces with variable exponent. The corresponding boundedness properties of their commutators with λ-central BMO symbols are also considered. Finally, we prove that the multilinear commutators of Calderón-Zygmund singular integrals introduced by Pérez and Trujillo-Gonález are bounded on central Morrey spaces with variable exponent. Our results improve and generalize some previous classical results to the variable exponent setting.

• Communications of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.719-722
• /
• 2022

In this paper, we present some estimates for the norm of a multilinear form T ∈ 𝓛(^m𝑙ⁿ_p) for 1 ≤ p ≤ ∞ and n, m ≥ 2.

• Journal of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.671-694
• /
• 2018

In this paper, we investigate the weighted vector-valued bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};\;{\mathbb{R}}^n,\;w_1){\times}{\cdots}{\times}L^{p_m}(l^{q_m};\;{\mathbb{R}}^n,\;w_m)$ to $L^p(l^q;\;{\mathbb{R}}^n,\;{\nu}_{\vec{w}})$, with $p_1,{\cdots},p_m$, $q_1,{\cdots},q_m{\in}(1,\;{\infty})$, $1/p=1/p_1+{\cdots}+1/p_m$, $1/q=1/q_1+{\cdots}+1/q_m$ and ${\vec{w}}=(w_1,{\cdots},w_m)$ a multiple $A_{\vec{P}}$ weights. Our argument also leads to the weighted weak type endpoint estimates for the commutators. As applications, we obtain some new weighted estimates for the $Calder{\acute{o}}n$ commutator.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.3
• /
• pp.1037-1067
• /
• 2017

Motzkin and Straus established a close connection between the maximum clique problem and a solution (namely graph-Lagrangian) to the maximum value of a class of homogeneous quadratic multilinear functions over the standard simplex of the Euclidean space in 1965. This connection and its extensions were successfully employed in optimization to provide heuristics for the maximum clique problem in graphs. It is useful in practice if similar results hold for hypergraphs. In this paper, we develop a homogeneous multilinear function based on the structure of hypergraphs and their complement hypergraphs. Its maximum value generalizes the graph-Lagrangian. Specifically, we establish a connection between the clique number and the generalized graph-Lagrangian of 3-uniform graphs, which supports the conjecture posed in this paper.