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On the Commutators of Marcinkiewicz Integral with a Function in Generalized Campanato Spaces on Generalized Morrey Spaces

Author

Listed:
  • Fuli Ku

    (School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
    College of Mathematics and Physics, Xinjiang Agricultural University, Urumqi 830054, China)

  • Huoxiong Wu

    (School of Mathematical Sciences, Xiamen University, Xiamen 361005, China)

Abstract

This paper is devoted to exploring the mapping properties for the commutator μ Ω , b generated by Marcinkiewicz integral μ Ω with a locally integrable function b in the generalized Campanato spaces on the generalized Morrey spaces. Under the assumption that the integral kernel Ω satisfies certain log-type regularity, it is shown that μ Ω , b is bounded on the generalized Morrey spaces with variable growth condition, provided that b is a function in generalized Campanato spaces, which contain the B M O ( R n ) and the Lipschitz spaces Lip α ( R n ) ( 0 < α ≤ 1 ) as special examples. Some previous results are essentially improved and generalized.

Suggested Citation

  • Fuli Ku & Huoxiong Wu, 2022. "On the Commutators of Marcinkiewicz Integral with a Function in Generalized Campanato Spaces on Generalized Morrey Spaces," Mathematics, MDPI, vol. 10(11), pages 1-14, May.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1817-:d:823853
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