• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.489-509
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• 2024

In this paper, let q ∈ (0, 1]. We establish the boundedness of intrinsic g-functions from the Hardy-Lorentz spaces with variable exponent H^p(·),q(ℝⁿ) into Lorentz spaces with variable exponent L^p(·),q(ℝⁿ). Then, for any q ∈ (0, 1], via some estimates on a discrete Littlewood-Paley g-function and a Peetre-type maximal function, we obtain several equivalent characterizations of H^p(·),q(ℝⁿ) in terms of wavelets.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.103-127
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• 2018

This paper is dedicated to studying some Hausdorff operators on the Heisenberg group ${\mathbb{H}}^n$. The sharp bounds on the strong-type weighted Lorentz spaces ${\Lambda}^p_u(w)$ and the weak-type weighted Lorentz spaces ${\Lambda}^{p,{\infty}}_u(w)$ are investigated. Especially, the results cover the classical power weighted space $L^{p,q}_{\alpha}$. The results are also extended to the product spaces ${\Lambda}^{p_1}_{u_1}(w_1){\times}{\Lambda}^{p_2}_{u_2}(w_2)$, especially for $L^{p_1,q_1}_{{\alpha}_1}{\times}L^{p_2,q_2}_{{\alpha}_2}$. Our proofs are quite different from those in previous documents since the duality principle, and some well-known inequalities concerning the weights are adopted. The results recover the existing results as well as we obtain new results in the new and old settings.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.85-92
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• 2021

In present paper, inspired by the recently paper [1], we give the mixed pressure-velocity regular criteria in view of Lorentz spaces for weak solutions to 3D micropolar equations in a half space. Precisely, if (0.1) ${\frac{P}{(e^{-{\mid}x{\mid}^2}+{\mid}u{\mid})^{\theta}}{\in}L^p(0,T;L^{q,{\infty}}({\mathbb{R}}^3_+))$, p, q < ∞, and (0.2) ${\frac{2}{p}}+{\frac{3}{q}}=2-{\theta}$, 0 ≤ θ ≤ 1, then (u, w) is regular on (0, T].

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.195-205
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• 2022

In this paper, we provide various characterizations for the composition operator on Lorentz spaces L(p, q), 1 < p ≤ ∞, 1 ≤ q ≤ ∞ to have finite ascent (descent) in terms of its inducing measurable transformation. At the end, in order to demonstrate our outcomes, some examples are given.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.701-708
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• 2007

In this paper we characterize the boundedness, compactness and closedness of the range of the weighted composition operators on Lorentz spaces L(p,q), $1.

• Kyungpook Mathematical Journal
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• v.11 no.1
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• pp.101-115
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• 1971

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.83-94
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• 1989

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.579-593
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• 2007

In this paper, we study some properties of ruled surfaces in a three-dimensional Lorentz-Minkowski space related to their Gaussian curvature, the second Gaussian curvature and the mean curvature. Furthermore, we examine the ruled surfaces in a three-dimensional Lorentz-Minkowski space satisfying the Jacobi condition formed with those curvatures, which are called the II-W and the II-G ruled surfaces and give a classification of such ruled surfaces in a three-dimensional Lorentz-Minkowski space.

• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.949-966
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• 2009

In this paper we introduce in study a new class of complex Finsler spaces, namely the complex Randers spaces, for which the fundamental metric tensor and the Chern-Finsler connection are determined. A special approach is devoted to $K{\ddot{a}}ahler$-Randers metrics. Using the length arc parametrization for the extremal curves of the Euler-Lagrange equations we obtain a complex nonlinear connections of Lorentz type in a complex Randers space.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2001-2011
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• 2017

In 1997, H. Li [12] proposed a conjecture: if $M^n(n{\geqslant}3)$ is a complete spacelike hypersurface in de Sitter space $S^{n+1}_1(1)$ with constant normalized scalar curvature R satisfying $\frac{n-2}{n}{\leqslant}R{\leqslant}1$, then is $M^n$ totally umbilical? Recently, F. E. C. Camargo et al. ([5]) partially proved the conjecture. In this paper, from a different viewpoint, we study closed convex spacelike hypersurface $M^n$ in locally symmetric Lorentz space $L^{n+1}_1$ and also prove that $M^n$ is totally umbilical if the square of length of second fundamental form of the closed convex spacelike hypersurface $M^n$ is constant, i.e., Theorem 1. On the other hand, we obtain that if the sectional curvature of the closed convex spacelike hypersurface $M^n$ in locally symmetric Lorentz space $L^{n+1}_1$ satisfies $K(M^n)$ > 0, then $M^n$ is totally umbilical, i.e., Theorem 2.