Littlewood-Paley theory and function spaces with \(A_p^{\text{loc}}\) weights (Q2721358)

As stated by the authors, the purpose of the paper is to develop the Littlewood-Paley theory for a class of weights satisfying the \(A_p\) condition restricted to cubes \(Q\) with \(|Q|\leq 1\) containing all \(A_p\) weights and also all locally regular weights up to exponential growth or decrease at infinity, in order to unify, generalize and simplify the known results. The crucial property is a local Calderón-type reproducing formula which enables to decompose distributions of arbitrary growth at infinity. Weighted Triebel-Lizorkin and Besov-Lipschitz spaces are then considered, and the author studies real interpolation and the action of Bessel potentials in these spaces. A last section is devoted to locally weighted Hardy spaces.