Abstract In this paper, we explore a general method to derive H p → L p boundedness from H p → H p boundedness of linear operators, an idea originated in the work of Han and Lu in dealing with the multiparameter flag singular integrals ([Discrete Littlewood-Paley-Stein theory and multi-parameter Hardy spaces associated with the flag singular integrals]). These linear operators include many singular integral operators in one parameter and multiparameter settings. In this paper, we will illustrate further that this method will enable us to prove the H p → L p boundedness on product spaces of homogeneous type in the sense of Coifman and Weiss ([Lecture Notes in Math. 242: 1971]) where maximal function characterization of Hardy spaces is not available. Moreover, we also provide a particularly easy argument in those settings such as one parameter or multiparameter Hardy spaces and where the maximal function characterization exists. The key idea is to prove ‖ƒ‖ L p ≤ C ‖ƒ ‖ H p for ƒ ∈ L q ∩ H p (1 < q < ∞, 0 < p ≤ 1). It is surprising that this simple result even in this classical setting has been absent in the literature.