Hardy spaces associated with ball quasi‐Banach function spaces on spaces of homogeneous type: Characterizations of maximal functions, decompositions, and dual spaces

Let ( X , ρ μ ) $({\mathcal {X}},\rho ,\mu )$ be a space of homogeneous type in the sense Coifman and Weiss, let Y $Y({\mathcal {X}})$ ball quasi-Banach function on ${\mathcal {X}}$ which supports both Fefferman–Stein vector-valued maximal inequality boundedness powered Hardy–Littlewood operator its associate space. The authors first introduce Hardy H ∗ $H_{Y}^*({\mathcal associated with via grand then establish various real-variable characterizations, respectively, terms radial or nontangential functions, atoms finite atoms, molecules. As an application, give dual proves to Campanato-type . All these results have wide range generality and, particularly, even when they are applied variable spaces, obtained also new. major novelties this paper exist that, escape reverse doubling condition triangle ρ, cleverly construct admissible sequences balls fully use geometrical properties expressed by dyadic reference points cubes overcome difficulty caused lack good dense subset further prove that can embedded into weighted Lebesgue certain special weight known