Boundedness and Compactness of Commutators for Bilinear Fractional Integral Operators on Morrey Spaces

Abstract

We show a characterization for the boundedness of the commutators for bilinear fractional integral operators Bα (0 < α < n) on Morrey spaces. Moreover, we obtain that if b ∈ CMO, then the commutators [b, Bα]i (i = 1, 2) are separately compact operators on Morrey spaces where CMO denotes the BMO-closure of C c (ℝn). A necessary condition for commutators [b, Bα]i (i = 1, 2) to be jointly compact on Morrey spaces is also given.

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Correspondence to J. Zhou.

Additional information

The research was supported by the National Natural Science Foundation of China (11661075).

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Guo, Q., Zhou, J. Boundedness and Compactness of Commutators for Bilinear Fractional Integral Operators on Morrey Spaces. Anal Math 47, 81–103 (2021). https://doi.org/10.1007/s10476-021-0067-9

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Key words and phrases

  • characterization
  • boundedness
  • bilinear fractional integral operator
  • Morrey space
  • compactness

Mathematics Subject Classification

  • primary 42B20
  • secondary 42B35
  • 42B99