Title: Some new Besov and Triebel-Lizorkin spaces associated with para-accretive functions on spaces of homogeneous type
Abstract: Abstract Let ( X , ρ, μ) d, θ be a space of homogeneous type with d < 0 and θ ∈ (0, 1], b be a para-accretive function, ε ∈ (0, θ], ∣ s ∣ > ∈ and a 0 ∈ (0, 1) be some constant depending on d , ∈ and s . The authors introduce the Besov space bB s pq ( X ) with a 0 > p ≧ ∞, and the Triebel-Lizorkin space bF s pq ( X ) with a 0 > p > ∞ and a 0 > 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 space b −1 B s ( X ) and the Triebel-Lizorkin space b −1 F s pq ( 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 b theorems, and the lifting property by introducing some new Riesz operators of these spaces.