Let X be a ball quasi-Banach function space on Rn\documentclass[12pt]{minimal}
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\begin{document}$${{\mathbb {R}}}^n$$\end{document} satisfying some mild assumptions. In this article, the authors first find a reasonable version T~\documentclass[12pt]{minimal}
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\begin{document}$$\widetilde{T}$$\end{document} of the Calderón–Zygmund operator T on the ball Campanato-type function space LX,q,s,d(Rn)\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {L}}_{X,q,s,d}({\mathbb {R}}^n)$$\end{document} with q∈[1,∞)\documentclass[12pt]{minimal}
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\begin{document}$$q\in [1,\infty )$$\end{document}, s∈Z+n\documentclass[12pt]{minimal}
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\begin{document}$$s\in {\mathbb {Z}}_+^n$$\end{document}, and d∈(0,∞)\documentclass[12pt]{minimal}
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\begin{document}$$d\in (0,\infty )$$\end{document}. Then the authors prove that T~\documentclass[12pt]{minimal}
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\begin{document}$$\widetilde{T}$$\end{document} is bounded on LX,q,s,d(Rn)\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {L}}_{X,q,s,d}({\mathbb {R}}^n)$$\end{document} if and only if, for any γ∈Z+n\documentclass[12pt]{minimal}
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\begin{document}$$\gamma \in {\mathbb {Z}}^n_+$$\end{document} with |γ|≤s\documentclass[12pt]{minimal}
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\begin{document}$$|\gamma |\le s$$\end{document}, T∗(xγ)=0\documentclass[12pt]{minimal}
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\begin{document}$$T^*(x^{\gamma })=0$$\end{document}, which is hence sharp. Moreover, T~\documentclass[12pt]{minimal}
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\begin{document}$$\widetilde{T}$$\end{document} is proved to be the adjoint operator of T, which further strengthens the rationality of the definition of T~\documentclass[12pt]{minimal}
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\begin{document}$$\widetilde{T}$$\end{document}. All these results have a wide range of applications. In particular, even when they are applied, respectively, to weighted Lebesgue spaces, variable Lebesgue spaces, Orlicz spaces, Orlicz-slice spaces, Morrey spaces, mixed-norm Lebesgue spaces, local generalized Herz spaces, and mixed-norm Herz spaces, all the obtained results are new. The proofs of these results strongly depend on the properties of the kernel of T under consideration and also on the dual theorem on LX,q,s,d(Rn)\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {L}}_{X,q,s,d}({\mathbb {R}}^n)$$\end{document}.
