Science in China Series A: Mathematics

, Volume 52, Issue 11, pp 2493–2505

Commutators of Littlewood-Paley operators

Article

DOI: 10.1007/s11425-009-0178-4

Cite this article as:
Chen, Y. & Ding, Y. Sci. China Ser. A-Math. (2009) 52: 2493. doi:10.1007/s11425-009-0178-4

Abstract

Let bLloc(ℝn) and L denote the Littlewood-Paley operators including the Littlewood-Paley g function, Lusin area integral and gλ* function. In this paper, the authors prove that the Lp boundedness of commutators [b, L] implies that b ∈ BMO(ℝn). The authors therefore get a characterization of the Lp-boundedness of the commutators [b, L]. Notice that the condition of kernel function of L is weaker than the Lipshitz condition and the Littlewood-Paley operators L is only sublinear, so the results obtained in the present paper are essential improvement and extension of Uchiyama’s famous result.

Keywords

Littlewood-Paley g function area integral gλ* function commutators BMO 

MSC(2000)

42B20 42B99 

Copyright information

© Science in China Press and Springer Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Mathematics and Mechanics, Applied Science SchoolUniversity of Science and Technology BeijingBeijingChina
  2. 2.School of Mathematical SciencesBeijing Normal UniversityBeijingChina
  3. 3.Laboratory of Mathematics and Complex Systems (BNU), Ministry of EducationBeijingChina

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