In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we prop...In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we propose to use these results for solution of equations with shift which arise in the study of cyclic models for natural systems with renewable resources.展开更多
We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or,...We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or, Gibbs-Butzer calculus）. Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D（C Kp） and locally compact group Kp^＋-（= Kp）, so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type, and equivalent approximation theorems on the HOlder-type space C^σ（Kp）, σ 〉0, are proved; then the equivalent approximation theorem on Sobolev-type space Wr（Kp）, σ≥0, 1≤r 〈∞, is shown.展开更多
In martingale setting, it has been shown thatA p weights can be factorized in terms ofA 1 weights. This factorization benefits many problems very much. In this paper, the new class of RH∞ plays the same role for RH s...In martingale setting, it has been shown thatA p weights can be factorized in terms ofA 1 weights. This factorization benefits many problems very much. In this paper, the new class of RH∞ plays the same role for RH s , which makes the reverse H?lder inequalities hold with exponents>1, that the classA 1 does forA p class. Therefore, the Jones' factorization theorem forA p weights was extended to include some information about the reverse H?lder classes. And it is the most convenient object in weight theory indeed. Key words martingale space - minimal function - weight inequality - reverse H?lder class CLC number O 221. 4 Foundation item: Supported by the National Natural Science Foundation of China (19771063)Biography: Zuo Hong-liang (1976-), male, Ph. D candidate, research direction: martingale theory.展开更多
Let A=-（ -ia）·（ -ia）＋V be a magnetic Schrodinger operator on L^2（R^n）,n〉2,where a：=（a1,…,an）∈Lloc^2（R^n,R^n） and 0≤V ∈Lloc^1（R^n）.In this paper, we show that for a function b in Lipschitz space...Let A=-（ -ia）·（ -ia）＋V be a magnetic Schrodinger operator on L^2（R^n）,n〉2,where a：=（a1,…,an）∈Lloc^2（R^n,R^n） and 0≤V ∈Lloc^1（R^n）.In this paper, we show that for a function b in Lipschitz space Lipa（R^n）with a∈（0,1）,the commutator [b,V1/2A^-1/2]is bounded from L^p（R^n）to L^q（R^n）,where p,q∈（1,2] and 1/p-1/q=a/n.展开更多
We introduce a new function space that is much finer than the classical Lebesgue spaces, and investigate the continuity and the discontinuity of the Calderon-Zygmund operators on the new weighted spaces. In order to i...We introduce a new function space that is much finer than the classical Lebesgue spaces, and investigate the continuity and the discontinuity of the Calderon-Zygmund operators on the new weighted spaces. In order to identify the continuity of singular integrals, we prove an interpolation theorem on the new spaces and propose a concept of the spectrum of base functions.展开更多
The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on t...The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on the Euclidean space R^n and the local field K are compared,so that one may interpret the essential differences between the analyses on R^n and K.Finally,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m＜(ln 2/ln 3).展开更多
In this paper we establish an interior regularity of weak solution for quasi-linear degenerate elliptic equations under the subcritical growth if its coefficient matrix A（x, u） satisfies a VMO condition in the varia...In this paper we establish an interior regularity of weak solution for quasi-linear degenerate elliptic equations under the subcritical growth if its coefficient matrix A（x, u） satisfies a VMO condition in the variable x uniformly with respect to all u, and the lower order item B（x, u, △↓u） satisfies the subcritical growth （1.2）. In particular, when F（x） ∈ L^q（Ω） and f（x） ∈ L^γ（Ω） with q,γ 〉 for any 1 〈 p 〈 ＋∞, we obtain interior HSlder continuity of any weak solution of （1.1） u with an index κ = min{1 - n/q, 1 - n/γ}.展开更多
文摘In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we propose to use these results for solution of equations with shift which arise in the study of cyclic models for natural systems with renewable resources.
文摘We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or, Gibbs-Butzer calculus）. Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D（C Kp） and locally compact group Kp^＋-（= Kp）, so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type, and equivalent approximation theorems on the HOlder-type space C^σ（Kp）, σ 〉0, are proved; then the equivalent approximation theorem on Sobolev-type space Wr（Kp）, σ≥0, 1≤r 〈∞, is shown.
基金Supported by the National Natural Science Foundation of China(19771063)
文摘In martingale setting, it has been shown thatA p weights can be factorized in terms ofA 1 weights. This factorization benefits many problems very much. In this paper, the new class of RH∞ plays the same role for RH s , which makes the reverse H?lder inequalities hold with exponents>1, that the classA 1 does forA p class. Therefore, the Jones' factorization theorem forA p weights was extended to include some information about the reverse H?lder classes. And it is the most convenient object in weight theory indeed. Key words martingale space - minimal function - weight inequality - reverse H?lder class CLC number O 221. 4 Foundation item: Supported by the National Natural Science Foundation of China (19771063)Biography: Zuo Hong-liang (1976-), male, Ph. D candidate, research direction: martingale theory.
基金supported by the National Natural Science Foundation of China (No.11671031 and No.11471018)the Fundamental Research Funds for the Central Universities (No.FRF-BR-17-004B)Program for New Century Excellent Talents in University,Beijing Municipal Science and Technology Project (No.Z17111000220000)
文摘Let A=-（ -ia）·（ -ia）＋V be a magnetic Schrodinger operator on L^2（R^n）,n〉2,where a：=（a1,…,an）∈Lloc^2（R^n,R^n） and 0≤V ∈Lloc^1（R^n）.In this paper, we show that for a function b in Lipschitz space Lipa（R^n）with a∈（0,1）,the commutator [b,V1/2A^-1/2]is bounded from L^p（R^n）to L^q（R^n）,where p,q∈（1,2] and 1/p-1/q=a/n.
文摘We introduce a new function space that is much finer than the classical Lebesgue spaces, and investigate the continuity and the discontinuity of the Calderon-Zygmund operators on the new weighted spaces. In order to identify the continuity of singular integrals, we prove an interpolation theorem on the new spaces and propose a concept of the spectrum of base functions.
基金This work supported by the National Natural Science Foundation of China(Grant No.10571084)
文摘The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on the Euclidean space R^n and the local field K are compared,so that one may interpret the essential differences between the analyses on R^n and K.Finally,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m＜(ln 2/ln 3).
基金National Natural Science Foundation of China (No.10671022)
文摘In this paper we establish an interior regularity of weak solution for quasi-linear degenerate elliptic equations under the subcritical growth if its coefficient matrix A（x, u） satisfies a VMO condition in the variable x uniformly with respect to all u, and the lower order item B（x, u, △↓u） satisfies the subcritical growth （1.2）. In particular, when F（x） ∈ L^q（Ω） and f（x） ∈ L^γ（Ω） with q,γ 〉 for any 1 〈 p 〈 ＋∞, we obtain interior HSlder continuity of any weak solution of （1.1） u with an index κ = min{1 - n/q, 1 - n/γ}.
