JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (4): 66-75.doi: 10.6040/j.issn.1671-9352.0.2020.195

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Boundedness for commutators of parameterized Marcinkiewicz integral on weighted Herz-Morrey spaces with variable exponent

XIN Yin-ping   

  1. School of Information Engineering, Lanzhou University of Finance and Economics, Lanzhou 730010, Gansu, China
  • Published:2021-04-13

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Abstract: The weighted boundedness of parameterized Marcinkiewicz integral on a class of generalized Lebesgue spaces with variable exponent is established. Furthermore, by using hierarchical decomposition of functions and the weighted inequalities, the boundedness of the higher order commutators generated by parameterized Marcinkiewicz integral and function of bounded mean oscillation(BMO)b on weighted Herz spaces and weighted Herz-Morrey spaces with variable exponent are obtained.

Key words: parameterized Marcinkiewicz integral, commutator, weighted variable exponent Herz space, weighted variable exponent Herz-Morrey space

CLC Number: 

  • O174.22
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