Higher Order Commutators of Marcinkiewicz Integral Operator on Herz-Morrey Spaces with Variable Exponent
Received:April 14, 2013  Revised:September 11, 2013
Key Words: Herz-Morrey spaces   Marcinkiewicz integral   commutator   variable exponent.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.\,) and the Natural Science Foundation of Anhui Higher Education Institutions (Grant Nos.KJ2011A138; KJ2013B034).
Author NameAffiliation
Liwei WANG School of Mathematics and Physics, Anhui Polytechnic University, Anhui 241000, P. R. China 
Lisheng SHU School of Mathematics and Computer Science, Anhui Normal University, Anhui 241003, P. R. China 
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Abstract:
      In the case of $\Omega\in {\rm Lip}_\gamma({{\mathbb S}^{n-1}})~(0<\gamma\leq1)$, we prove the boundedness of the Marcinkiewicz integral operator $\mu_{\Omega}$ on the variable exponent Herz-Morrey spaces. Also, we prove the boundedness of the higher order commutators $\mu^{m}_{\Omega,b}$ with $b\in {{\rm BMO}({\mathbb R}^n)}$ on both variable exponent Herz spaces and Herz-Morrey spaces, and extend some known results.
Citation:
DOI:10.3770/j.issn:2095-2651.2014.02.007
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