In this paper,using inhomogeneous Calderon’s reproducing formulas and the space of test functions associated with a para-accretive function,the inhomogeneous Besov and TriebelLizorkin spaces are established.As applic...In this paper,using inhomogeneous Calderon’s reproducing formulas and the space of test functions associated with a para-accretive function,the inhomogeneous Besov and TriebelLizorkin spaces are established.As applications,pointwise multiplier theorems are also obtained.展开更多
There are two folds in this article. One fold is to characterize the Besov spaces of para-accretive type , which reduces to the classical Besov spaces when the para-accretive function is constant, by using a discrete ...There are two folds in this article. One fold is to characterize the Besov spaces of para-accretive type , which reduces to the classical Besov spaces when the para-accretive function is constant, by using a discrete Calderón-type reproducing formula and Plancherel-P?lya-type inequality associated to a para-accretive function b in Rn. The other is to show that a generalized singular integral operator T with extends to be bounded from for and , where ε is the regularity exponent of the kernel of T.展开更多
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 the...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).展开更多
基金supported by the National Natural Science Foundation of China(11901495)Hunan Provincial NSF Project(2019JJ50573)the Scientific Research Fund of Hunan Provincial Education Department(22B0155)。
文摘In this paper,using inhomogeneous Calderon’s reproducing formulas and the space of test functions associated with a para-accretive function,the inhomogeneous Besov and TriebelLizorkin spaces are established.As applications,pointwise multiplier theorems are also obtained.
文摘There are two folds in this article. One fold is to characterize the Besov spaces of para-accretive type , which reduces to the classical Besov spaces when the para-accretive function is constant, by using a discrete Calderón-type reproducing formula and Plancherel-P?lya-type inequality associated to a para-accretive function b in Rn. The other is to show that a generalized singular integral operator T with extends to be bounded from for and , where ε is the regularity exponent of the kernel of T.
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.
文摘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).
