The atomic decomposition for tent spaces on spaces of homogeneous type

By E. Russ. 2007

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Orlicz-Hardy Spaces Associated with Operators Satisfying Davies-Gaffney Estimates (2009, unknown): “Thus, for j = 0, 1, 2, we obtain Hj . sup 0≤k≤M ∥∥∥∥ ∫ δ 0 (t2L)(M+1)e−2t 2LLM̃−kb(x) dt t ∥∥∥∥ L2(Uj(B)) (4.10) . sup 0≤k≤M [ M∑ i=1 ‖(δ2L)ie−2δ2L(LM̃−kb)‖L2(Uj(B)) +‖(e−2δ2L − I)(LM̃−kb)‖L2(Uj(B)) ] → 0, as δ → 0.”
Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates (2013, background): “The tent space T p 2 (X+) on spaces of homogenous type was introduced by Russ [65].”
Hardy Spaces of Differential Forms on Riemannian Manifolds (2006, background): “It turns out that every F ∈ T 1,2( T ∗M) has an atomic decomposition (see, [40]).”
Musielak–Orlicz–Hardy Spaces Associated with Operators and Their Applications (2012, background): “The tent space T p2 (X × (0,∞)) on spaces of homogenous type was introduced by Russ [82].”
Hardy spaces associated to operators satisfying Davies–Gaffney estimates and bounded holomorphic functional calculus☆ (2013, methodology): “[ 7 ] P. Auscher and E. Russ, Hardy spaces and divergence operators on strongly Lipschitz domains of Rn, J. Funct.”