Hardy type spaces estimates for multilinear fractional integral operators

In this paper, we prove the boundedness of multilinear fractional integral operators from products of Hardy spaces associated with ball quasi-Banach function spaces into their corresponding ball quasi-Banach function spaces. As applications, we establish the boundedness of these operators on various function spaces, including weighted Hardy spaces, variable Hardy spaces, mixed-norm Hardy spaces, Hardy–Lorentz spaces, and Hardy–Orlicz spaces. Notably, several of these results are new, even in special cases, and extend the existing theory of multilinear operators in the context of generalized Hardy spaces.