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arXiv · 1604.07037

Non-homogeneous $Tb$ Theorem for Bi-parameter $g$-Function

Mingming Cao·Qingying Xue
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Abstract

The main result of this paper is a bi-parameter $Tb$ theorem for Littlewood-Paley $g$-function, where $b$ is a tensor product of two pseudo-accretive functions. Instead of the doubling measure, we work with a product measure $\mu = \mu_n \times \mu_m$, where the measures $\mu_n$ and $\mu_m$ are only assumed to be upper doubling. The main techniques of the proof include a bi-parameter $b$-adapted Haar function decomposition and an averaging identity over good double Whitney regions. Moreover, the non-homogeneous analysis and probabilistic methods are used again.

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Mingming Cao, Qingying Xue. 2016-04-24. Non-homogeneous $Tb$ Theorem for Bi-parameter $g$-Function. https://arxiv.org/abs/1604.07037

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