Maximal function characterizations of Hardy spaces on RD-spaces and their applications

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Weighted anisotropic product Hardy spaces and boundedness of sublinear operators (2009, background): “As an application, we prove that if T is a sublinear operator and maps all (p, q, ~s)∗w-atoms into uniformly bounded elements of a quasi-Banach space B, then T uniquely extends to a bounded sublinear operator from Hpw(Rn × Rm; ~A) to B.”
REAL-VARIABLE CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BESSEL OPERATORS (2011, background): “1 by directly applying results in [14, 10, 27].”
Localized BMO and BLO Spaces on RD-Spaces and Applications to Schr\ (2009, methodology): “It was proved in [31] that if f ∈ H1 ρ(X ), the Hardy space associated to ρ, then f−Kρ(f) ∈ H1(X ), where H1(X ) is the Hardy space studied in [15, 16, 14], which coincides with the atomic Hardy space H1 at(X ) of Coifman and Weiss in [3].”
On the ¹–¹ boundedness of operators (2008, result): “For so-called RD-spaces, which are spaces of homogeneous type having “dimen-sion n ” in a certain sense, our complete results were recently extended in the paper [9] by L. Grafakos, L. Liu and Yang.”
Weighted anisotropic Hardy spaces and their applications in boundedness of sublinear operators (2008, result): “These results were generalized in [ 20 ] to Hardy spacesHp withp close to 1 on spaces of homogeneous type having the reverse doubling property.”