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2015•Taiwanese Journal of MathematicsOpen access

COMMUTATORS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS ON NON-HOMOGENEOUS METRIC MEASURE SPACES

Rulong Xie, Huajun Gong, Xiaoyao Zhou

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Abstract

Let $(X,d,\mu)$ be a metric measure space satisfying both thegeometrically doubling and the upper doubling measure conditions,which is called non-homogeneous metric measure space. In thispaper, via a sharp maximal operator, the boundedness of commutatorsgenerated by multilinear singular integral with $RBMO(\mu)$ functionon non-homogeneous metric measure spaces in $m$-multiple Lebesgue spacesis obtained.

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Let $(X,d,\mu)$ be a metric measure space satisfying both thegeometrically doubling and the upper doubling measure conditions,which is called non-homogeneous metric measure space. In thispaper, via a sharp maximal operator, the boundedness of commutatorsgenerated by multilinear singular integral with $RBMO(\mu)$ functionon non-homogeneous metric measure spaces in $m$-multiple Lebesgue spacesis obtained.

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Available abstract

Let $(X,d,\mu)$ be a metric measure space satisfying both thegeometrically doubling and the upper doubling measure conditions,which is called non-homogeneous metric measure space. In thispaper, via a sharp maximal operator, the boundedness of commutatorsgenerated by multilinear singular integral with $RBMO(\mu)$ functionon non-homogeneous metric measure spaces in $m$-multiple Lebesgue spacesis obtained.

Key concepts: Mathematics, Multilinear map, Singular integral operators, Measure (data warehouse), Homogeneous, Metric (unit), Pure mathematics, Singular integral

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COMMUTATORS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS ON NON-HOMOGENEOUS METRIC MEASURE SPACES — Research Paper | ScholarLens