A New Approach for Hardy Spaces on Euclidean Space

In this paper, we develop a new approach to the classical Hardy spaces on Euclidean space. The new ideas of this paper are (i) introduce new test functions and distributions; (ii) we use the classical Calderón reproducing formula on \(L^2({\mathbb {R}}^d)\) $L^2({\mathbb{R}}^d)$ only; (iii) the Hardy space is defined by the collections of all new distributions with the classical wavelet-type representation and the norms of Hardy space are defined as the norms of the classical atomic Hardy spaces.