$H^{p}$ spaces associated with Schrödinger operators with potentials from reverse Hölder classes
By Jacek Dziubański, J. Zienkiewicz. 2003
112 citations recorded by the source corpus.
Let A = −∆ + V be a Schrödinger operator on R, d ≥ 3, where V is a nonnegative potential satisfying the reverse Hölder inequality with an exponent q > d/2. We say that f is an element of H A if the maximal function supt>0 |Ttf(x)| belongs to L(R), where {Tt}t>0 is the semigroup generated by −A. It is proved that for d/(d+1) < p ≤ 1 the space H A admits a special atomic decomposition.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/184a96ccdf2d87e80749c7beb84a63b85bbe3f0a
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In Applied Mathematics
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Citations in the corpus
- Riesz transforms related to Schrödinger operators acting on BMO type spaces (2009, background): “Such space is defined through the following function associated to V already used in [4, 5, 6, 12].”
- Classes of Hardy spaces associated with operators, duality theorem and applications (2008, unknown): “In [20], Hardy spaces associated with Schrödinger operators were studied.”
- Localized BMO and BLO Spaces on RD-Spaces and Applications to Schr\ (2009, background): “Then we have the following estimates; see [8, 6, 7].”
- Orlicz-Hardy Spaces Associated with Operators Satisfying Davies-Gaffney Estimates (2009, background): “Moreover, if n = 1 and p = 1, the Hardy space H1L(R n) coincides with the Hardy space introduced by Czaja and Zienkiewicz in [9]; if L = −∆ + V and V belongs to the reverse Hölder class Hq(Rn) for some q ≥ n/2 with n ≥ 3, then the Hardy spaceHpL(Rn) when p ∈ (n/(n+1), 1] coincides with the Hardy sp”