Let X be a ball quasi-Banach function space on Rⁿ, WX be the weak ball quasi-Banach function space on Rⁿ, hX be the local Hardy space associated with X. In this paper, we introduce the weak local Hardy-type space W hX associated with X via using maximal function characterization. Moreover, we obtain the boundedness of in homogeneous Calder? n-Zygmund operators from hX to WX or W hX. All these results have a wide range of generality and, particularly, to our best knowledge, even when they are applied to the Morrey spaces, Orlicz-slice spaces and mixed-norm Lebesgue spaces, the results in this paper are also new.
Liu et al. (2025) studied this question.