Some new Triebel-Lizorkin spaces on spaces of homogeneous type and their frame characterizations  

作　　者：YANG Dachun 

机构地区：[1]Department of Mathematics,Beijing Normal University,Beijing 100875,China

出　　处：《Science China Mathematics》2005年第1期12-39,共28页中国科学：数学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.10271015);the Research Fund for the Doctoral Program of Higher Education(Grant No.20020027004)of China.

摘　　要：Let(χ,ρ,μ)_d,θ be a space of homogeneous type,∈∈(0,θ],|s|<∈andmax{d/(d+∈),d/(d+s+∈)}<q≤∞.The author introduces the new Triebel-Lizorkin spaces F_∞q^s(X)and establishes the framecharacterizations of these spaces by first establishing a Plancherel-P(?)lya-type inequalityrelated to the norm of the spaces F_∞q^s(X).The frame characterizations of the Besovspace B_pq^s(X)with |s|<∈,max{d/(d+∈),d/(d+s+∈)}<p≤∞ and 0<q ≤∞and the Triebel-Lizorkin space F_spq^s(X)with |s|<∈,max{d/(d+∈),d/(d+s+∈)}<p<∞ and max{d/(d+∈),d/(d+s+∈)}<q≤∞ are also presented.Moreover,the au-thor introduces the new Triebel-Lizorkin spaces bF_∞q^s(X)and HF_∞q^s(X)associated to agiven para-accretive function b.The relation between the space bF_∞q^s(X)and the spaceHF_∞q^s(X)is also presented.The author further proves that if s=0 and q=2,thenHF_∞q^s(X)=F_∞q^s(X),which also gives a new characterization of the space BMO(X),since F_∞q^s(X)=BMO(X).Let(X,ρ,μ)d,θ be a space of homogeneous type,ε∈ (0,θ],|s|＜εand max{d/(d +ε),d/(d+s+ε)}＜q≤∞.The author introduces the new Triebel-Lizorkin spaces Fs∞q(X) and establishes the frame characterizations of these spaces by first establishing a Plancherel-Polya-type inequality related to the norm of the spaces Fs∞q(X).The frame characterizations of the Besov space Bspq(X) with |s|＜ε,max{d/(d+ε),d/(d+s+ε)}＜p≤∞ and 0＜q≤∞ and the Triebel-Lizorkin space Fspq(X) with |s|＜ε,max {d/(d+ε),d/(d+s+ε)}＜p＜∞ and max{d/(d+ε),d/(d+s+ε)}＜q≤∞ are also presented.Moreover,the author introduces the new Triebel-Lizorkin spaces bFs∞q(X) and HFs∞q(X) associated to a given para-accretive function b.The relation between the space bFs∞q(X) and the space 0 and q=2,then resented.The author further proves that if s=HFs∞q(X) is also pHFs∞q(X) = Fs∞q(X),which also gives a new characterization of the space BMO(X),since Fs∞q(X)=BMO(X).

关 键 词：space of homogeneous type Plancherel-Polya inequality Triebel-Lizorkin space Carleson maximal function Calderón reproducing formula para-accretive function BMO(X) 

分 类 号：N[自然科学总论]