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Anisotropic singular integrals in product spaces

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Abstract

In this paper, the authors introduce a class of product anisotropic singular integral operators, whose kernels are adapted to the action of a pair \( \vec A \):= (A 1, A 2) of expansive dilations on ℝn and ℝm, respectively. This class is a generalization of product singular integrals with convolution kernels introduced in the isotropic setting by Fefferman and Stein. The authors establish the boundedness of these operators in weighted Lebesgue and Hardy spaces with weights in product A ∞ Muckenhoupt weights on ℝn × ℝm. These results are new even in the unweighted setting for product anisotropic Hardy spaces.

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Authors and Affiliations

  1. School of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, China

    BaoDe Li

  2. Department of Mathematics, University of Oregon, Eugene, OR, 97403-1222, USA

    Marcin Bownik

  3. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, China

    DaChun Yang & Yuan Zhou

Authors
  1. BaoDe Li
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  2. Marcin Bownik
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  3. DaChun Yang
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  4. Yuan Zhou
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Correspondence to DaChun Yang.

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Li, B., Bownik, M., Yang, D. et al. Anisotropic singular integrals in product spaces. Sci. China Math. 53, 3163–3178 (2010). https://doi.org/10.1007/s11425-010-4108-2

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