• Korean Journal of Mathematics
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• 제16권4호
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• pp.495-498
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• 2008

Every totally disconnected space is hereditarily disconnected. In this note, we provide an example of a hereditarily disconnected which is not a totally disconnected space. We further provide an example that not homogeneous space is the product of a totally disconnected and a connected.

• 대한수학회보
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• 제17권1호
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• pp.21-24
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• 1980

• East Asian mathematical journal
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• 제13권2호
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• pp.149-157
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• 1997

• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.377-387
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• 2006

In this paper, we study the $L^p$ mapping properties of singular integral operators related to homogeneous mappings on product spaces with kernels which belong to $L(log^+\;L)^2$. Our results extend as well as improve some known results on singular integrals.

• 대한수학회보
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• 제56권6호
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• pp.1377-1384
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• 2019

In this paper, we prove that for every surjective phase-isometry between the unit spheres of real atomic $L_p$-spaces for p > 0, its positive homogeneous extension is a phase-isometry which is phase equivalent to a linear isometry.

• 대한수학회지
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• 제61권2호
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• pp.341-356
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• 2024

In this paper, apply the regularities of the fractional Poisson kernels, we establish the Sobolev type trace inequalities of homogeneous Besov spaces, which are invariant under the conformal transforms. Also, by the aid of the Carleson measure characterizations of Q type spaces, the local version of Sobolev trace inequalities are obtained.

• 대한수학회지
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• 제35권2호
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• pp.361-370
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• 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.

• East Asian mathematical journal
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• 제16권2호
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• pp.183-197
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• 2000

• 대한수학회지
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• 제57권3호
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• pp.721-745
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• 2020

In this paper we study fractional Sobolev spaces characterized by a norm based on eigenfunction expansions. The goal of this paper is twofold. The first one is to define fractional Sobolev spaces of order -1 ≤ s ≤ 2 equipped with a norm defined in terms of Neumann eigenfunction expansions. Due to the zero Neumann trace of Neumann eigenfunctions on a boundary, fractional Sobolev spaces of order 3/2 ≤ s ≤ 2 characterized by the norm are the spaces of functions with zero Neumann trace on a boundary. The spaces equipped with the norm are useful for studying cross-sectional traces of solutions to the Helmholtz equation in waveguides with a homogeneous Neumann boundary condition. The second one is to define fractional Sobolev spaces of order -1 ≤ s ≤ 1 for vector-valued functions in a simply-connected, bounded and smooth domain in ℝ². These spaces are defined by a norm based on series expansions in terms of eigenfunctions of the vector Laplacian with boundary conditions of zero tangential component or zero normal component. The spaces defined by the norm are important for analyzing cross-sectional traces of time-harmonic electromagnetic fields in perfectly conducting waveguides.

• 호남수학학술지
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• 제33권4호
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• pp.557-573
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• 2011

Let G be a compact and connected semisimple Lie group, H a closed subgroup, g (resp. h) the Lie algebra of G (resp. H), B the Killing form of g, g the normal metric on the homogeneous space G/H which is induced by -B. Let D be an invarint connection with Weyl structure (D, g, ${\omega}$) in the tangent bundle over the normal homogeneous Riemannian manifold (G/H, g) which is projectively flat. Then, the affine connection D on (G/H, g) is a Yang-Mills connection if and only if D is the Levi-Civita connection on (G/H, g).