• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.435-452
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• 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
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• v.49 no.5
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• pp.907-925
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• 2012

In this paper the boundedness for a large class of multi-sublinear operators is established on product generalized Morrey spaces with non-doubling measures. As special cases, the corresponding results for multilinear Calder$\acute{o}$n-Zygmund operators, multilinear fractional integrals and multi-sublinear maximal operators will be obtained.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.851-864
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• 2020

This paper gives a sparse domination for the iterated commutators of multilinear pseudo-differential operators with the symbol σ belonging to the Hörmander class, and establishes the quantitative bounds of the Bloom type estimates for such commutators. Moreover, the C_p estimates for the corresponding multilinear pseudo-differential operators are also obtained.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.565-570
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• 2020

We investigate the best equivalence constants for the 𝑙_p-norms and the 𝑙_q-symmetric multilinear operator norms of vectors in ℂⁿ which are induced by symmetric n-linear forms. In this paper, we provides estimates which are either best possible or close to best possible.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.195-212
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• 2023

In this paper, two weight conditions are introduced and the multiple weighted strong and weak characterizations of the multilinear fractional new maximal operator 𝓜_ϕ,β are established. Meanwhile, we introduce the ${\mathcal{S}}_{({\vec{p}},q),{\beta}}({\varphi})$ and $B_{({\vec{p}},q),{\beta}}({\varphi})$ conditions and obtain the characterization of two-weighted inequalities for 𝓜_ϕ,β. Finally, the relationships of the conditions ${\mathcal{S}}_{({\vec{p}},q),{\beta}}({\varphi}),\,{\mathcal{A}}_{({\vec{p}},q),{\beta}}({\varphi})$ and $B_{({\vec{p}},q),{\beta}}({\varphi})$ and the characterization of the one-weight $A_{({\vec{p}},q),{\beta}}({\varphi})$ are given.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.541-560
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• 2023

Let T be an m-linear Calderón-Zygmund operator. $T_{{\vec{b}S}}$ is the generalized commutator of T with a class of measurable functions {b_i}^∞_i=1. In this paper, we will give some new estimates for $T_{{\vec{b}S}}$ when {b_i}^∞_i=1 belongs to Orlicz-type space and Lipschitz space, respectively.

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

• Coupled systems mechanics
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• v.12 no.5
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• pp.409-418
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• 2023

A coupled algorithm is proposed which first considers the creation of porous structure of the material and then the simulations of response of mechanical components with porous structure to a variable load history. The simulations are carried out by the Prandtl operator approach in the finite element method (FEM) which enables structural simulations of mechanical components subjected to variable thermomechanical loads. Temperature-dependent material properties and multilinear kinematic hardening of the material can be taken into account by this approach. Several simulations are then performed for a tensile-compressive specimen made of a generic porous structure and mechanical properties of Aluminium alloy AlSi9Cu3. Variable mechanical load history has been applied to the specimens under constant temperature conditions. Comparison of the simulation results shows a considerable elastoplastic stress-strain response in the vicinity of pores whilst the surface of the gauge-length of the specimen remains in the elastic region of the material. Moreover, the distribution of the pore sizes seems more influential to the stress-strain field during the loading than their radial position in the gauge-length.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.23 no.2
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• pp.132-141
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• 2024

In this study, the differences in user satisfaction and the variables influencing the satisfaction with demand response transport (DRT) by travel purpose were compared. The purpose of DRT travel was divided into commuting/school and shopping/leisure travel. A survey conducted on 'Shucle' users in Sejong City was used for the analysis and the least absolute shrinkage and selection operator (LASSO) regression analysis was applied to minimize the overfitting problems of the multilinear model. The results of the analysis confirmed the possibility that the introduction of the DRT service could eliminate the blind spot in the existing public transportation, reduce the use of private cars, encourage low-carbon and public transportation revitalization policies, and provide optimal transportation services to people who exhibit intermittent travel behaviors (e.g., elderly people, housewives, etc.). In addition, factors such as the waiting time after calling a DRT, travel time after boarding the DRT, convenience of using the DRT app, punctuality of expected departure/arrival time, and location of pickup and drop-off points were the common factors that positively influenced the satisfaction of users of the DRT services during their commuting/school and shopping/leisure travel. Meanwhile, the method of transfer to other transport modes was found to affect satisfaction only in the case of commuting/school travel, but not in the case of shopping/leisure travel. To activate the DRT service, it is necessary to consider the five influencing factors analyzed above. In addition, the differentiating factors between commuting/school and shopping/leisure travel were also identified. In the case of commuting/school travel, people value time and consider it to be important, so it is necessary to promote the convenience of transfer to other transport modes to reduce the total travel time. Regarding shopping/leisure travel, it is necessary to consider ways to create a facility that allows users to easily and conveniently designate the location of the pickup and drop-off point.