Riesz transforms associated to Schrdinger operators on weighted Hardy spaces

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Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates (2013, background): “Very recently, the authors of this paper [12] studied the weighted Hardy space associated with nonnegative self-adjoint operators satisfying the reinforced off-diagonal estimates on Rn (see Assumption (B) for their definitions in the present setting), which improves those results in [17, 67, 74] in ”
Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their Applications (2012, methodology): “Moreover, different from [48, 8], we do not need the additional assumption that for any t ∈ [0,∞), φ(·, t) satisfies the reverse Hölder inequality of order 2 (see Definition 2.”
Musielak–Orlicz–Hardy Spaces Associated with Operators and Their Applications (2012, methodology): “More precisely, in [86], the atomic characterization of the weighted Hardy space H1 L(R n), associated with the Schrödinger operator L, was established by using the Calderón reproducing formula associated with L and a subtle decomposition of all dyadic cubes in Rn.”