Littlewood-Paley-Stein functions on complete Riemannian manifolds for 1 ≤ p ≤ 2
Thierry Coulhon, Xuan Thinh Duong, Xiang Dong Li (2003)
Studia Mathematica
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We study the weak type (1,1) and the -boundedness, 1 < p ≤ 2, of the so-called vertical (i.e. involving space derivatives) Littlewood-Paley-Stein functions and ℋ respectively associated with the Poisson semigroup and the heat semigroup on a complete Riemannian manifold M. Without any assumption on M, we observe that and ℋ are bounded in , 1 < p ≤ 2. We also consider modified Littlewood-Paley-Stein functions that take into account the positivity of the bottom of the spectrum....