Multilinear operators on Hardy spaces associated with ball quasi-Banach function spaces

This paper establishes that multilinear Calderón–Zygmund operators and their maximal operators are bounded on Hardy spaces associated with ball quasi-Banach function spaces. Moreover, we also obtain the boundedness of multilinear pseudo-differential operators on local Hardy spaces associated with ball quasi-Banach function spaces. Since these (local) Hardy type spaces encompass a wide range of classical (local) Hardy-type spaces including weighted (local) Hardy spaces, variable (local) Hardy space, (local) Hardy–Morrey space, mixed-norm (local) Hardy space, (local) Hardy–Lorentz space and (local) Hardy–Orlicz spaces, the results presented in this paper are highly general and essentially improve the existing results.