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2010•Chinese Annals of MathematicsRequires access

The Boundedness of the Commutators for Marcinkiewicz Integrals with Non-doubling Measures

Xiaoli Chen

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Abstract

In this paper,the authors prove that the commutators of Marcinkiewicz integralM_b has not only the(L~p(μ),L~q(μ))-boundedness but also the(L~1(μ),L~(q,∞)(μ))-boundedness.On the other hand,the(L~p(μ),Lip_(β-(n/p))-boundedness and the(L~(n/β)(μ),RBMO(μ))-boundedness of M_b are also obtained.

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What this paper is about

In this paper,the authors prove that the commutators of Marcinkiewicz integralM_b has not only the(L~p(μ),L~q(μ))-boundedness but also the(L~1(μ),L~(q,∞)(μ))-boundedness.On the other hand,the(L~p(μ),Lip_(β-(n/p))-boundedness and the(L~(n/β)(μ),RBMO(μ))-boundedness of M_b are also obtained.

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Available abstract

In this paper,the authors prove that the commutators of Marcinkiewicz integralM_b has not only the(L~p(μ),L~q(μ))-boundedness but also the(L~1(μ),L~(q,∞)(μ))-boundedness.On the other hand,the(L~p(μ),Lip_(β-(n/p))-boundedness and the(L~(n/β)(μ),RBMO(μ))-boundedness of M_b are also obtained.

Key concepts: Mathematics, Commutator, Pure mathematics, Mathematical analysis, Algebra over a field, Lie conformal algebra

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