The Multilinear Littlewood–Paley Operators with Minimal Regularity Conditions

  • Mingming Cao
  • Kôzô Yabuta


We investigate the quantitative weighted estimates for a large class of the multilinear Littlewood–Paley square operators. Our kernels satisfy the minimal regularity assumption, called \(L^r\)-Hörmander condition. We respectively establish the pointwise sparse domination for the multilinear square functions and their iterated commutators. Based on them, we obtain the strong type quantitative bounds and endpoint estimates. We recover lots of known weighted inequalities for Littlewood–Paley operators. Significantly, the approach is dyadic, quite elementary and simpler than that presented previously.


Multilinear Sparse operators Littlewood–Paley functions Quantitative weighted estimates 

Mathematics Subject Classification

Primary 42B25 Secondary 42B20 



The authors would like to thank the referee for valuable suggestions which have improved the quality of this paper.


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Authors and Affiliations

  1. 1.Laboratory of Mathematics and Complex Systems, Ministry of Education, School of Mathematical SciencesBeijing Normal UniversityBeijingPeople’s Republic of China
  2. 2.Research Center for Mathematical SciencesKwansei Gakuin UniversitySandaJapan

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