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2010•Analysis in Theory and ApplicationsRequires access

Estimates for the maximal multilinear singular integral operators

Yulan Jiao

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Abstract

In this paper, some mapping properties are considered for the maximal multilinear singular integral operator whose kernel satisfies certain minimum regularity condition. It is proved that certain uniform local estimate for doubly truncated operators implies the L p (R n ) (1 < p < ∞) boundedness and a weak type LlogL estimate for the corresponding maximal operator.

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What this paper is about

In this paper, some mapping properties are considered for the maximal multilinear singular integral operator whose kernel satisfies certain minimum regularity condition. It is proved that certain uniform local estimate for doubly truncated operators implies the L p (R n ) (1 < p < ∞) boundedness and a weak type LlogL estimate for the corresponding maximal operator.

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Available abstract

In this paper, some mapping properties are considered for the maximal multilinear singular integral operator whose kernel satisfies certain minimum regularity condition. It is proved that certain uniform local estimate for doubly truncated operators implies the L p (R n ) (1 < p < ∞) boundedness and a weak type LlogL estimate for the corresponding maximal operator.

Key concepts: Multilinear map, Mathematics, Singular integral operators, Maximal operator, Singular integral, Operator (biology), Kernel (algebra), Maximal function

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