Acta mathematica scientia,Series A ›› 2018, Vol. 38 ›› Issue (4): 716-727.

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Boundedness of the Intrinsic Square Function on Variable Exponent Herz and Herz-Hardy Spaces

Wang Liwei1, Shu Lisheng2   

  1. 1 School of Mathematics and Physics, Anhui Polytechnic University, Anhui Wuhu 241000;
    2 School of Mathematics and Computer Science, Anhui Normal University, Anhui Wuhu 241003
  • Received:2017-08-09 Revised:2017-12-18 Online:2018-08-26 Published:2018-08-26
  • Supported by:
    Supported by the NSFC (11771223)

Abstract: In this paper, we show that the intrinsic square function Sβ is bounded on the variable exponent Herz spaces Kp(·)α(·), q(Rn) and Herz-Hardy spaces HKp(·)α(·), q(Rn), where α(·) and p(·) are variable. In particular, when α(·) ≡ α is constant, the corresponding main results are also new.

Key words: The intrinsic square function, Variable Herz spaces, Variable Herz-Hardy spaces

CLC Number: 

  • O174.2
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