• Title/Summary/Keyword: Marcinkiewicz integral operators

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On the Boundedness of Marcinkiewicz Integrals on Variable Exponent Herz-type Hardy Spaces

  • Heraiz, Rabah
    • Kyungpook Mathematical Journal
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    • v.59 no.2
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    • pp.259-275
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    • 2019
  • 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 $H{\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$.

PARABOLIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO POLYNOMIALS COMPOUND CURVES AND EXTRAPOLATION

  • Liu, Feng;Zhang, Daiqing
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.3
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    • pp.771-788
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    • 2015
  • In this note we consider the parametric Marcinkiewicz integrals with mixed homogeneity along polynomials compound curves. Under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction, the $L^p$ bounds of such operators are given by an extrapolation argument. Some previous results are greatly extended and improved.