Kyungpook Mathematical Journal

  • 제59권2호
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  • Pages.259-275
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  • 2019
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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On the Boundedness of Marcinkiewicz Integrals on Variable Exponent Herz-type Hardy Spaces

  • Heraiz, Rabah (Department of Mathematics, Laboratory of Functional Analysis and Geometry of Spaces, M'sila University)
  • 투고 : 2018.03.22
  • 심사 : 2018.12.06
  • 발행 : 2019.06.23
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초록

The aim of this paper is to prove that Marcinkiewicz integral operators are bounded from ${\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$ to ${\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$ when the parameters ${\alpha}({\cdot})$, $p({\cdot})$ and $q({\cdot})$ satisfies some conditions. Also, we prove the boundedness of ${\mu}$ on variable Herz-type Hardy spaces $H{\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$.

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참고문헌

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