Abstract
AbstractLet (X, ρ, μ)d, θbe a space of homogeneous type withd< 0 and θ ∈ (0, 1],bbe a para-accretive function, ε ∈ (0, θ], ∣s∣ > ∈ and a0∈ (0, 1) be some constant depending ond, ∈ ands. The authors introduce the Besov spacebBspq(X) with a0> p ≧ ∞, and the Triebel-Lizorkin spacebFspq(X) with a0>p> ∞ and a0> q ≧∞ by first establishing a Plancherel-Pôlya-type inequality. Moreover, the authors establish the frame and the Littlewood-Paley function characterizations of these spaces. Furthermore, the authors introduce the new Besov spaceb−1Bs(X) and the Triebel-Lizorkin spaceb−1Fspq(X). The relations among these spaces and the known Hardy-type spaces are presented. As applications, the authors also establish some real interpolation theorems, embedding theorems,T btheorems, and the lifting property by introducing some new Riesz operators of these spaces.
Publisher
Cambridge University Press (CUP)
Cited by
7 articles.
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