• Title/Summary/Keyword: Herz-hardy space

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COMMUTATORS OF SINGULAR INTEGRAL OPERATOR ON HERZ-TYPE HARDY SPACES WITH VARIABLE EXPONENT

  • Wang, Hongbin
    • Journal of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.713-732
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    • 2017

  • Let ${\Omega}{\in}L^s(S^{n-1})$ for s > 1 be a homogeneous function of degree zero and b be BMO functions or Lipschitz functions. In this paper, we obtain some boundedness of the $Calder{\acute{o}}n$-Zygmund singular integral operator $T_{\Omega}$ and its commutator [b, $T_{\Omega}$] on Herz-type Hardy spaces with variable exponent.

  • https://doi.org/10.4134/JKMS.j150771 인용 PDF KSCI

BOUNDEDNESS FOR FRACTIONAL HARDY-TYPE OPERATOR ON HERZ-MORREY SPACES WITH VARIABLE EXPONENT

  • Wu, Jianglong
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.2
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    • pp.423-435
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    • 2014

  • In this paper, the fractional Hardy-type operator of variable order ${\beta}(x)$ is shown to be bounded from the Herz-Morrey spaces $M\dot{K}^{{\alpha},{\lambda}}_{p_1,q_1({\cdot})}(\mathbb{R}^n)$ with variable exponent $q_1(x)$ into the weighted space $M\dot{K}^{{\alpha},{\lambda}}_{p_2,q_2({\cdot})}(\mathbb{R}^n,{\omega})$, where ${\omega}=(1+|x|)^{-{\gamma}(x)}$ with some ${\gamma}(x)$ > 0 and $1/q_1(x)-1/q_2(x)={\beta}(x)/n$ when $q_1(x)$ is not necessarily constant at infinity. It is assumed that the exponent $q_1(x)$ satisfies the logarithmic continuity condition both locally and at infinity that 1 < $q_1({\infty}){\leq}q_1(x){\leq}(q_1)+$ < ${\infty}(x{\in}\mathbb{R}^n)$.

  • https://doi.org/10.4134/BKMS.2014.51.2.423 인용 PDF KSCI