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 function. Instead of the doubling measure, we work with a product measure μ = μn × μm, where the measures μn and μm 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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The authors would like to thank the referee for valuable suggestions which improved the readability of this article.
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Supported by NSFC (Grant No. 11471041)
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Cao, M.M., Xue, Q.Y. Non-homogeneous Tb Theorem for Bi-parameter g-function. Acta. Math. Sin.-English Ser. 34, 1445–1459 (2018). https://doi.org/10.1007/s10114-018-7431-0
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DOI: https://doi.org/10.1007/s10114-018-7431-0