• Title, Summary, Keyword: homogeneous type space

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[ $L^p$ ] NORM INEQUALITIES FOR AREA FUNCTIONS WITH APPROACH REGIONS

  • Suh, Choon-Serk
    • East Asian mathematical journal
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    • v.21 no.1
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    • pp.41-48
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    • 2005
  • In this paper we first introduce a space of homogeneous type X, and then consider a kind of generalized upper half-space $X{\times}(0,\;\infty)$. We are mainly considered with inequalities for the $L^p$ norms of area functions associated with approach regions in $X{\times}(0,\;\infty)$.

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Infinite element for the scaled boundary analysis of initial valued non-homogeneous elastic half space (초기치를 갖는 비동질무한영역의 해석을 위한 비례경계무한요소법)

  • Lee, Gye-Hee;Deeks, Andrew J.
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.259-264
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    • 2007
  • In this paper, to analyze the initial valued non-homogeneous elastic half space by the scaled boundary analysis, the infinite element approach was introduced. The free surface of the initial valued non-homogeneous elastic half space was mode1ed as a circumferential direction of boundary scaled boundary coordinate. The infinite element was used to represent the infinite length of the free surface. The initial value of material property(elastic modulus) was considered by the combination of the position of the sealing center and the power function of the radial direction. By use of the mapping type infinite element, the consistent e1ements formulation could be available. The performance and the feasibility of proposed approach are examined by two numerical examples.

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A DECOMPOSITION INTO ATOMS OF TENT SPACES ASSOCIATED WITH GENERAL APPROACH REGIONS

  • Suh, Choon-Serk
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.3
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    • pp.453-461
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    • 2010
  • We first introduce a space of homogeneous type X, and develop the theory of the tent spaces on the generalized upper half-space $X{\times}(0,{\infty})$. The goal of this paper is to study that every element of the tent spaces $T_{\Omega}^{p}$($X{\times}(0,{\infty})$, $0, can be decomposed into elementary particles which are called "atoms."

A STUDY ON CARLESON MEASURES WITH RESPECT TO GENERAL APPROACH REGIONS

  • Suh, Choon-Serk
    • Communications of the Korean Mathematical Society
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    • v.17 no.1
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    • pp.31-36
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    • 2002
  • In this paper we first introduce a space of homogeneous type X, and we consider a kind of generalized upper half-space X $\times$ (0, $\infty$). We are mainly concerned with some inequalities in terms of Carleson measures or in terms of certain maximal operators with respect to general approach regions in X $\times$ (0, $\infty$). The main tool of the proof is the Whitney decomposition.

ON MAXIMAL OPERATORS BELONGING TO THE MUCKENHOUPT'S CLASS $A_1$

  • Suh, Choon-Serk
    • East Asian mathematical journal
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    • v.23 no.1
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    • pp.37-43
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    • 2007
  • We study a maximal operator defined on spaces of homogeneous type, and we prove that this operator is of weak type (1,1). As a consequence we show that the maximal operator belongs to the Muckenhoupt's class $A_1$.

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Infinite Element for the Scaled Boundary Analysis of Initial Valued on-Homogeneous Elastic Half Space (초기값을 갖는 비동질무한영역의 해석을 위한 비례경계무한요소법)

  • Lee, Gye-Hee;Deeks, Andrew J.
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.21 no.2
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    • pp.199-208
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    • 2008
  • In this paper, to analyze the initial valued non-homogeneous elastic half space by the scaled boundary analysis, the infinite element approach was introduced. The free surface of the initial valued non-homogeneous elastic half space was modeled as a circumferential direction of boundary scaled boundary coordinate. The infinite element was used to represent the infinite length of the free surface. The initial value of material property(elastic modulus) was considered by the combination of the position of the scaling center and the power function of the radial direction. By use of the mapping type infinite element, the consistent elements formulation could be available. The performance and the feasibility of proposed approach are examined by two numerical examples.

MODULI SPACES OF ORIENTED TYPE ${\mathcal{A}}$ MANIFOLDS OF DIMENSION AT LEAST 3

  • Gilkey, Peter;Park, JeongHyeong
    • Journal of the Korean Mathematical Society
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    • v.54 no.6
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    • pp.1759-1786
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    • 2017
  • We examine the moduli space of oriented locally homogeneous manifolds of Type ${\mathcal{A}}$ which have non-degenerate symmetric Ricci tensor both in the setting of manifolds with torsion and also in the torsion free setting where the dimension is at least 3. These exhibit phenomena that is very different than in the case of surfaces. In dimension 3, we determine all the possible symmetry groups in the torsion free setting.