• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.315-328
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• 2006

In this paper, the Boundedness for the multilinear Littlewood-Paley operator on certain Hardy and Herz-Hardy spaces are obtained.

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

• 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.

• Kyungpook Mathematical Journal
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• v.12 no.1
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• pp.27-28
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• 1972

• 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.