Non-homogeneous <Emphasis Type="Italic">Tb</Emphasis> Theorem for Bi-parameter <Emphasis Type="Italic">g</Emphasis>-function |
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Authors: | Ming Ming Cao Qing Ying Xue |
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Institution: | School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China |
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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 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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Keywords: | Bi-parameter square function probabilistic method b-adapted Haar functions |
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