Applications of Hardy Spaces Associated with Ball Quasi-Banach Function Spaces

Let X be a ball quasi-Banach function space satisfying some minor assumptions. In this article, the authors establish the characterizations of H-X(R-n), the Hardy space associated with X, via the LittlewoodPaley g-functions and g(lambda)*-functions. Moreover, the authors obtain the boundedness of Calderon-Zygmund operators on H-X(R-n). For the local Hardy-type space h(X)(R-n) associated with X, the authors also obtain the boundedness of S-1,0(0)(R-n) pseudo-differential operators on h(X)(R-n) via first establishing the atomic characterization of h(X)(R-n). Furthermore, the characterizations of h(X)(R-n) by means of local molecules and local Littlewood-Paley functions are also given. The results obtained in this article have a wide range of generality and can be applied to the classical Hardy space, the weighted Hardy space, the Herz-Hardy space, the Lorentz-Hardy space, the Morrey-Hardy space, the variable Hardy space, the Orlicz-slice Hardy space and their local versions. Some special cases of these applications are even new and, particularly, in the case of the variable Hardy space, the g(lambda)*-function characterization obtained in this article improves the known results via widening the range of lambda.