Littlewood–Paley Theory and Function Spaces with Alocp Weights

Characterizations via convolutions with smooth compactly supported kernels and other distinguished properties of the weighted Besov–Lipschitz and Triebel–Lizorkin spaces on ?ⁿ with weights that are locally in A_p but may grow or decrease exponentially at infinity are investigated. Square–function characterizations of the weighted L^p and Hardy spaces with the above class of weights are also obtained. A certain local variant of the Calderón reproducing formula is constructed and widely used in the proofs.