• Title/Summary/Keyword: spaces of homogeneous type

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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 FOURIER MULTIPLIER THEOREM ON THE BESOV-LIPSCHITZ SPACES

  • Cho, Yong-Kum;Kim, Dohie
    • Korean Journal of Mathematics
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    • v.16 no.1
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    • pp.85-90
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    • 2008
  • We consider Fourier multiplier operators whose symbols satisfy a generalization of $H{\ddot{o}}rmander^{\prime}s$ condition and establish their Sobolev-type mapping properties on the homogeneous Besov-Lipschitz spaces by making use of a continuous characterization of Besov-Lipschitz spaces. As an application, we derive Sobolev-type imbedding theorem.

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WEKGHTED WEAK TYPE ESTIMATES FOR CERTAIN MAXIMAL OPERATORS IN SPACES OF HOMOGENEOUS TYPE

  • Yoo, Yoon-Jae
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.1
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    • pp.25-31
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    • 1999
  • Let $\nu$ be a positive Borel measure on a space of homogeneous type (X, d, $\mu$), satisfying the doubling property. A condition on a weight $\omega$ for whixh a maximal operator $M\nu f$(x) defined by M$mu$f(x)=supr>0{{{{ { 1} over {ν(B(x,r)) } INT _{ B(x,r)} │f(y)│d mu (y)}}}}, is of weak type (p,p) with respect to (ν, $omega$), is that there exists a constant C such that C $omega$(y) for a.e. y$\in$B(x, r) if p=1, and {{{{( { 1} over { upsilon (B(x,r) } INT _{ B(x,r)}omega(y) ^ (-1/p-1) d mu (y))^(p-1)}}}} C, if 1$infty$.

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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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A NOTE ON SOBOLEV TYPE TRACE INEQUALITIES FOR s-HARMONIC EXTENSIONS

  • Yongrui Tang;Shujuan Zhou
    • Journal of the Korean Mathematical Society
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    • v.61 no.2
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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.

WEAK TYPE INEQUALITY FOR POISSON TYPE INTEGRAL OPERATORS

  • Yoo, Yoon-Jae
    • Journal of the Korean Mathematical Society
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    • v.35 no.2
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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.

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