Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (3): 739-747.doi: 10.1016/S0252-9602(14)60045-X

• Articles • Previous Articles     Next Articles

AREA INTEGRAL FUNCTIONS FOR SECTORIAL OPERATORS ON Lp SPACES

 CHEN Ze-Qan, SUN Mu   

  1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, 30 West District, Xiao-Hong-Shan, Wuhan 430071, China|Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, 30 West District, Xiao-Hong-Shan, Wuhan 430071, China|School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2013-02-27 Online:2014-05-20 Published:2014-05-20
  • Supported by:

    Chen is partially supported by NSFC grant No. 11171338.

Abstract:

Area integral functions are introduced for sectorial operators on Lp-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on Lp spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H1 functional calculus of sectorial operators on Lp-spaces hold true when the square functions are replaced by the area integral functions.

Key words: Sectorial operator, H&infin, Functional calculus, area integral function, square function, Lp space

CLC Number: 

  • 47D06
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