Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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MAPPING PROPERTIES OF THE MARCINKIEWICZ INTEGRALS ON HOMOGENEOUS GROUPS

  • Published : 2002.01.01
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Abstract

Under the cancellation property and the Lipschitz condition on kernels, we prove that the Marcinkiewicz integrals defined on a homogeneous group H are bounded from $H^1$(H) to $L^1$(H), from $L_{c}$ $^{\infty}$(H) to BMO (H), and from $L^{p}$ (H) to $L^{p}$ (H) for 1 < p < $\infty$ assuming the $L^{q}$ -boundedness for some q > 1.for some q > 1.

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References

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