Abstract
In this paper, we consider the boundedness on Triebel-Lizorkin spaces for the d-dimensional Calderón commutator defined by
where Ω is homogeneous of degree zero, integrable on Sd−1 and has a vanishing moment of order one, and a is a function on \({\mathbb{R}^d}\) such that \(\nabla a \in {L^\infty }({\mathbb{R}^d})\). We prove that if 1 < p, q < ∞ and \(\Omega \in L{(\log L)^{2\tilde q}}({S^{d - 1}})\) with \(\tilde q = \max \{ 1/q,\,\,1/{q^\prime }\} \), then TΩ, a is bounded on Triebel-Lizorkin spaces \(\dot F_p^{0,q}({\mathbb{R}^d})\).
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The authors declare no conflict of interest.
The research was supported by the NNSF of China (11871108).
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Hu, G., Liu, J. Boundedness of the Calderón Commutator with a Rough Kernel on Triebel-Lizorkin Spaces. Acta Math Sci 43, 1618–1632 (2023). https://doi.org/10.1007/s10473-023-0411-1
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DOI: https://doi.org/10.1007/s10473-023-0411-1