A Representation Theorem for Singular Integral Operators on Spaces of Homogeneous Type

Details A Representation Theorem for Singular Integral Operators on Spaces of Homogeneous Type A Representation Theorem for Singular Integral Operators on Spaces of Homogeneous Type

2010-01-27

arxiv.org/abs/1001.4926v2

Mathematics

Functional Analysis

Scientific paper

Let (X,d,\mu) be a space of homogeneous type and E a UMD Banach space. Under
the assumption mu({x})=0 for all x in X, we prove a representation theorem for
singular integral operators on (X,d,mu) as a series of simple shifts and
rearrangements plus two paraproducts. This gives a T(1) Theorem in this
setting.

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