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2014•Unpublished venueRequires access

Boundedness of commtuators of parametric Marcinkiewicz integrals on Hardy spaces with non-doubling measures

Jian Zhou

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Abstract

In this paper,the authors prove the boundedness of the commutator M_b~p generated by the parameter Marcinkiewicz integral M~p with Lipschitz function 6.Under the assumption that the kernel of M satisfies certain condition,the authors prove that M_b~p is bounded from the Lebesgue space L~(n/(n-β))(μ) to the Hardy space H~1(μ),and from the Lebesgue space L~(n/β)(μ) to the space RBMO(μ).

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What this paper is about

In this paper,the authors prove the boundedness of the commutator M_b~p generated by the parameter Marcinkiewicz integral M~p with Lipschitz function 6.Under the assumption that the kernel of M satisfies certain condition,the authors prove that M_b~p is bounded from the Lebesgue space L~(n/(n-β))(μ) to the Hardy space H~1(μ),and from the Lebesgue space L~(n/β)(μ) to the space RBMO(μ).

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Available abstract

In this paper,the authors prove the boundedness of the commutator M_b~p generated by the parameter Marcinkiewicz integral M~p with Lipschitz function 6.Under the assumption that the kernel of M satisfies certain condition,the authors prove that M_b~p is bounded from the Lebesgue space L~(n/(n-β))(μ) to the Hardy space H~1(μ),and from the Lebesgue space L~(n/β)(μ) to the space RBMO(μ).

Key concepts: Mathematics, Hardy space, Lipschitz continuity, Commutator, Lebesgue integration, Lp space, Standard probability space, Bounded function

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