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2011•Journal of Mathematical InequalitiesOpen access

Boundedness for multilinear commutators of integral operators in Hardy and Herz-Hardy spaces on homogeneous spaces

Xianyi Chen, Lanzhe Liu

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Abstract

In this paper, we shall study the Hardy-boundedness for the multilinear commutators related to the singular integral operators on the space of homogeneous type. By using the Hlder's inequalities and the L q (1 < q < ) boundedness for the singular integral operators on the space of homogeneous type, we obtain the (H p b ,L p ) and (H K,p q, b , K,p q ) type boundedness for the multilinear commutators on the space of homogeneous type.

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In this paper, we shall study the Hardy-boundedness for the multilinear commutators related to the singular integral operators on the space of homogeneous type. By using the Hlder's inequalities and the L q (1 < q < ) boundedness for the singular integral operators on the space of homogeneous type, we obtain the (H p b ,L p ) and (H K,p q, b , K,p q ) type boundedness for the multilinear commutators on the space of homogeneous type.

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Available abstract

In this paper, we shall study the Hardy-boundedness for the multilinear commutators related to the singular integral operators on the space of homogeneous type. By using the Hlder's inequalities and the L q (1 < q < ) boundedness for the singular integral operators on the space of homogeneous type, we obtain the (H p b ,L p ) and (H K,p q, b , K,p q ) type boundedness for the multilinear commutators on the space of homogeneous type.

Key concepts: Multilinear map, Mathematics, Hardy space, Singular integral operators, Homogeneous, Type (biology), Singular integral, Pure mathematics

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