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A note on certain square functions on product spaces

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Abstract

We study certain square functions on product spaces ℝn×ℝm, whose integral kernels are obtained from kernels which are homogeneous in each factor ℝn and ℝm locally in L(log+ L) away from ℝn×{0} and ℝm by means of polynomial distortions in the radial variable. As a model case, we obtain that the Marcinkiewicz integral operator is bounded on L p(ℝn×ℝm)(p>1) for Ω∈Llog+ L(S n−1×S m−1) satisfying the cancellation condition.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University (at Yuquan campus), Hangzhou, 310027, China

    Wang Meng

  2. Department of Mathematics, Zhejiang University (at Xixi campus), Hangzhou, 310028, China

    Chen Jiecheng

  3. Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI53201, USA

    Fan Dashan

Authors
  1. Wang Meng
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  2. Chen Jiecheng
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  3. Fan Dashan
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Wang, M., Chen, J. & Fan, D. A note on certain square functions on product spaces. SCI CHINA SER A 49, 98–108 (2006). https://doi.org/10.1007/s11425-005-0101-6

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  • DOI: https://doi.org/10.1007/s11425-005-0101-6

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