JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (12): 45-54.doi: 10.6040/j.issn.1671-9352.0.2021.685

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Parameterized Littlewood-Paley operators with rough kernel on grand variable Herz spaces

SHI Peng-wei, TAO Shuang-ping*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2022-12-05

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Abstract: With the help of the boundedness of the Lebesgue space with variable exponent, by applying hierarchical decomposition of function and real variable techniques, the boundedness of the parameterized Marcinkiewicz integral, the area integral and Littlewood-Paley g*λ function with rough kernel is obtained on grand variable Herz spaces. Meanwhile, the boundedness of higher order commutators generated by the area integral and Littlewood-Paley g*λ function is also proved on grand variable Herz spaces.

Key words: grand variable Herz space, rough kernel, parameterized Littlewood-Paley operator, higher order commutator

CLC Number: 

  • O174.2
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