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Commutators of Bilinear θ-Type Calderón–Zygmund Operators on Morrey Spaces Over Non-Homogeneous Spaces

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Abstract

The aim of this paper is to establish the boundedness of the commutator [b1, b2, Tθ], which generated by the bilinear θ-type Calderón–Zygmund operators Tθ and the functions \(b_1, b_2 \in \widetilde {RBMO}(\mu)\), on non-homogeneous metric measure space satisfying the so-called geometrically doubling and the upper doubling conditions. Under the assumption that the dominating function λ satisfies the ε-weak reverse doubling conditions, the author proves that the commutator [b1, b2, Tθ] is bounded from the Lebesgue space Lp(μ) into the product of Lebesgue space \({L^{{p_1}}}(\mu ) \times {L^{{p_2}}}(\mu )\) with \(\frac{1}{p} = \frac{1}{{{p_1}}} + \frac{1}{{{p_2}}}(1 < p,{p_1},{p_2} < \infty )\). Furthermore, the boundedness of the commutator [b1, b2, Tθ] on Morrey space \(M_p^q(\mu)\) is also obtained, where 1 < qp < ∞.

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Author information

Correspondence to G.-H. Lu.

Additional information

This research was supported by the Doctoral Scientific Research Foundation of Northwest Normal University (No. 0002020203).

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Cite this article

Lu, G. Commutators of Bilinear θ-Type Calderón–Zygmund Operators on Morrey Spaces Over Non-Homogeneous Spaces. Anal Math 46, 97–118 (2020). https://doi.org/10.1007/s10476-020-0020-3

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Key words and phrases

  • non-homogeneous metric measure space
  • commutator
  • bilinear θ-type Calderón–Zygmund operator
  • \(\widetilde {RBMO}(\mu)\)
  • Morrey space

Mathematics Subject Classification

  • primary 42B20
  • secondary 46E30
  • 42B35
  • 30L99