Hardy spaces on homogeneous groups. (English) Zbl 0508.42025

Folland, G. B.; Stein, Elias M.

Mathematical Notes, 28. Princeton, New Jersey: Princeton University Press; University of Tokyo Press. XII, 284 p. $ 17.00 (1982).

MSC:

42B30	\(H^p\)-spaces
46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47F05	General theory of partial differential operators
42B25	Maximal functions, Littlewood-Paley theory
42B20	Singular and oscillatory integrals (Calderón-Zygmund, etc.)
43A30	Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.

Keywords:

homogeneous group; nilpotent; dilations; stratified; Hardy spaces; homogeneous norm; covering; heat operator; heat semigroup; maximal functions; grand maximal functions; maximal Hp spaces; atomic Hp spaces; Calderon-Zygmund decomposition; real interpolation; commutative convolution algebra; hypoelliptic G-invariant differential operator; Heisenberg group; Companato space; Lipschitz spaces; singular and fractional integrals; homogeneous dimension; kernels of type (alpha,r); homogeneous kernels; sublaplacian; boundary values; Poisson kernel