We consider the boundedness of the rough singular integral operator T_（？,ψ,h） along a surface of revolution on the Triebel-Lizorkin space F^α_（ p,q）（R^n） for Ω ∈ H^1（（S^n-1）） and Ω ∈ Llog^＋L（S^n-1）...We consider the boundedness of the rough singular integral operator T_（？,ψ,h） along a surface of revolution on the Triebel-Lizorkin space F^α_（ p,q）（R^n） for Ω ∈ H^1（（S^n-1）） and Ω ∈ Llog^＋L（S^n-1） ∪_1展开更多
We study the maximal super-singular integral operator T＊Ω,α,β（f）（x,y）=sup ∈1〉0,∈2〉0｜∫｜u｜〉ε1,｜v｜〉ε2 b1（｜u｜）b2（｜u｜）Ω（u＇,u＇）/｜u｜^n＋α｜u｜^m＋β-f（x-u,y-u）dudu｜defined on all f ...We study the maximal super-singular integral operator T＊Ω,α,β（f）（x,y）=sup ∈1〉0,∈2〉0｜∫｜u｜〉ε1,｜v｜〉ε2 b1（｜u｜）b2（｜u｜）Ω（u＇,u＇）/｜u｜^n＋α｜u｜^m＋β-f（x-u,y-u）dudu｜defined on all f ∈ S（R^n ×R^m）, where 0 ≤ α,β〈∞, b1 b2 ∈ L∞（R＋1 ）,Ω satisfies certain cancellation conditions and Ω∈L1（S^n-1×S^m-1）in the case α,β〉0;Ω∈L（log＋L）（S^n-1×S^m-1）in the case αβ=0 and α＋β 〉0. It is proved that, for 1〈p〈∞.T＊Ω,α,βis a bounded operator from the homogeneous Sobolev space Lα,β^p（R^n×R^m）to the Lebesgue space L^p（R^n×R^m）.展开更多
This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kern...This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.展开更多
We investigate the boundedness of singular and fractional integral operators on generalized Hardy spaces defined on spaces of homogeneous type, which are preduals of Campanato spaces with variable growth condition. To...We investigate the boundedness of singular and fractional integral operators on generalized Hardy spaces defined on spaces of homogeneous type, which are preduals of Campanato spaces with variable growth condition. To do this we introduce molecules with variable growth condition. Our results are new even for R^n case.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11371057, 11471033 and 11571160)Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20130003110003)+2 种基金the Fundamental Research Funds for the Central Universities (Grant No. 2014KJJCA10)Grant-in-Aid for Scientific Research (C) (Grant No. 23540228)Japan Society for the Promotion of Science
文摘We consider the boundedness of the rough singular integral operator T_（？,ψ,h） along a surface of revolution on the Triebel-Lizorkin space F^α_（ p,q）（R^n） for Ω ∈ H^1（（S^n-1）） and Ω ∈ Llog^＋L（S^n-1） ∪_1
基金supported by National Natural Science Foundation of China (Grant Nos. 10871173, 10931001)
文摘We study the maximal super-singular integral operator T＊Ω,α,β（f）（x,y）=sup ∈1〉0,∈2〉0｜∫｜u｜〉ε1,｜v｜〉ε2 b1（｜u｜）b2（｜u｜）Ω（u＇,u＇）/｜u｜^n＋α｜u｜^m＋β-f（x-u,y-u）dudu｜defined on all f ∈ S（R^n ×R^m）, where 0 ≤ α,β〈∞, b1 b2 ∈ L∞（R＋1 ）,Ω satisfies certain cancellation conditions and Ω∈L1（S^n-1×S^m-1）in the case α,β〉0;Ω∈L（log＋L）（S^n-1×S^m-1）in the case αβ=0 and α＋β 〉0. It is proved that, for 1〈p〈∞.T＊Ω,α,βis a bounded operator from the homogeneous Sobolev space Lα,β^p（R^n×R^m）to the Lebesgue space L^p（R^n×R^m）.
基金Project supported by the National Natural Science Foundation of China (No. 10001027).
文摘This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.
基金supported by Grant-in-Aid for Scientific Research (B) (Grant No. 15H03621), Japan Society for the Promotion of Science
文摘We investigate the boundedness of singular and fractional integral operators on generalized Hardy spaces defined on spaces of homogeneous type, which are preduals of Campanato spaces with variable growth condition. To do this we introduce molecules with variable growth condition. Our results are new even for R^n case.
