Operator h-preinvex functions are introduced and a refinement of HermiteHadamard type inequalities for such functions is established. Results proved in this paper are more general and some known results are special ca...Operator h-preinvex functions are introduced and a refinement of HermiteHadamard type inequalities for such functions is established. Results proved in this paper are more general and some known results are special cases.展开更多
In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditio...In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.展开更多
By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several propertie...By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several properties and characteristics including(for example)the modified Hadamard products,Holder's inequalities and convolution properties as well as some closure properties under a general family of integral transforms.展开更多
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates...Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .展开更多
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates...Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .展开更多
In this paper, we introduce new subclasses Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）of certain p-valent analytic functions defined by a generalized differential operator. Majorizationproperties for functions bel...In this paper, we introduce new subclasses Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）of certain p-valent analytic functions defined by a generalized differential operator. Majorizationproperties for functions belonging to the classes Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）are investigated. Also, we point out some new or known consequences of our main results.展开更多
A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α...A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α,β）by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class SHPλ（α,β） These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.展开更多
We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applic...We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.展开更多
Making use of the Carlson-Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigate inclusion relations, coefficie...Making use of the Carlson-Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. We also show that this class is closed under convolution with a convex function. Some applications are also discussed.展开更多
In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf（z） be a nonconstant entire function of ...In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf（z） be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f（z）, f（z＋c）, and △n cf（z） share 0 CM, then f（z＋c）≡Af（z）, where A（≠0） is a complex constant. Moreover, let a（z）, b（z）（ O） ∈ S（f） be periodic entire functions with period c and if f（z） - a（z）, f（z ＋ c） - a（z）, △cn f（z） - b（z） share 0 CM, then f（z ＋ c） ≡ f（z）.展开更多
As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimat...As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimates for weighted approximation of functions with singularities by Bernstein operators. The main results are the Jackson＇s estimates of functions f∈ （Wwλ）2 andre Cw, which extends the result of （Della Vecchia et al., 2004）.展开更多
The staggered-grid finite-difference （SGFD） method has been widely used in seismic forward modeling. The precision of the forward modeling results directly affects the results of the subsequent seismic inversion and...The staggered-grid finite-difference （SGFD） method has been widely used in seismic forward modeling. The precision of the forward modeling results directly affects the results of the subsequent seismic inversion and migration. Numerical dispersion is one of the problems in this method. The window function method can reduce dispersion by replacing the finite-difference operators with window operators, obtained by truncating the spatial convolution series of the pseudospectral method. Although the window operators have high precision in the low-wavenumber domain, their precision decreases rapidly in the high-wavenumber domain. We develop a least squares optimization method to enhance the precision of operators obtained by the window function method. We transform the SGFD problem into a least squares problem and find the best solution iteratively. The window operator is chosen as the initial value and the optimized domain is set by the error threshold. The conjugate gradient method is also adopted to increase the stability of the solution. Approximation error analysis and numerical simulation results suggest that the proposed method increases the precision of the window function operators and decreases the numerical dispersion.展开更多
In this paper, the author gives a characterization of atomic Hardy spaces associated to Schrodinger operators by using area functions, and hence gets the dual spaces of atomic Hardy spaces.
Let Hn(p)be the class of functions of the form f(z)=z p+ +∞Σ k=n akzk+p,which are analytic in the open unit disk U={z:|z|<1}.In the paper,we introduce a new subclass Bn(μ,a,c,α,p;φ)of Hn(p)and investigate its ...Let Hn(p)be the class of functions of the form f(z)=z p+ +∞Σ k=n akzk+p,which are analytic in the open unit disk U={z:|z|<1}.In the paper,we introduce a new subclass Bn(μ,a,c,α,p;φ)of Hn(p)and investigate its subordination relations,inclusion relations and distortion theorems.The results obtained include the related results of some authors as their special case.展开更多
In this paper,We mainly discuss some subclasses of analytic functions for operators onac, and determine a representation formula and sufficient condition for the class 4;(a.p,r,E,7) and prove a sufficient and necessar...In this paper,We mainly discuss some subclasses of analytic functions for operators onac, and determine a representation formula and sufficient condition for the class 4;(a.p,r,E,7) and prove a sufficient and necessary condition.coefficient estimates and distortiontheorem for the subclass O;o (a,p,Y,e,9) of the class ac;(a,p,y,c,V).Furthermore,the analogues also are true for operators on Hilbert space.展开更多
Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the re...Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions.展开更多
Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the...Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.展开更多
In this article, we prove the boundedness of commutators generated by BochnerRiesz operators below the critical index and BMO functions on the class of radial functions in Lp（Rn） with ｜1/p-1/2｜〈（1＋2α）/（2n）.
In this paper, we consider a general nonlinear integral operator Hαi, βi （ f1,..., fn ; g1,..., gn）（z）. Some results including coefficient problems, univalency condition and radius of convexity for this integral...In this paper, we consider a general nonlinear integral operator Hαi, βi （ f1,..., fn ; g1,..., gn）（z）. Some results including coefficient problems, univalency condition and radius of convexity for this integral operator are given. Furthermore, we discuss the mapping properties between Hαi,βi （f1 , fn, ; g1,..., gn）（z） and subclasses of analytic functions with bounded boundary rotation. The same subjects for some corresponding classes are shown upon specializing the parameters in our main results.展开更多
In this paper, we establish two weighted integral inequalities for commutators of fractional Hardy operators with Besov-Lipschitz functions. The main result is that this kind of commutator, denoted by H^ab, is bounded...In this paper, we establish two weighted integral inequalities for commutators of fractional Hardy operators with Besov-Lipschitz functions. The main result is that this kind of commutator, denoted by H^ab, is bounded from L^Pxy （R＋） to L^qxδ （R＋） with the bound explicitly worked out.展开更多
基金The NSF(11801342) of Chinathe Foundation(18JK0116) of Shaanxi Educational Committee
文摘Operator h-preinvex functions are introduced and a refinement of HermiteHadamard type inequalities for such functions is established. Results proved in this paper are more general and some known results are special cases.
基金supported by the National Natural Science Foundation of China(12171373)Chen's work also supported by the Fundamental Research Funds for the Central Universities of China(GK202207018).
文摘In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.
文摘By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several properties and characteristics including(for example)the modified Hadamard products,Holder's inequalities and convolution properties as well as some closure properties under a general family of integral transforms.
文摘Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .
文摘Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .
基金Supported by the National Natural Science Foundation of China(Grant No.11271045)the Funds of Doctoral Programme of China(Grant No.20100003110004)the Natural Science Foundation of Inner Mongolia Province(Grant No.2010MS0117)
文摘In this paper, we introduce new subclasses Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）of certain p-valent analytic functions defined by a generalized differential operator. Majorizationproperties for functions belonging to the classes Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）are investigated. Also, we point out some new or known consequences of our main results.
基金Supported by the Key Scientific Research Fund of Inner Mongolian Educational Bureau (NJ04115)
文摘A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α,β）by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class SHPλ（α,β） These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.
文摘We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.
文摘Making use of the Carlson-Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. We also show that this class is closed under convolution with a convex function. Some applications are also discussed.
基金supported by the Natural Science Foundation of Guangdong Province in China(2014A030313422,2016A030310106,2016A030313745)
文摘In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf（z） be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f（z）, f（z＋c）, and △n cf（z） share 0 CM, then f（z＋c）≡Af（z）, where A（≠0） is a complex constant. Moreover, let a（z）, b（z）（ O） ∈ S（f） be periodic entire functions with period c and if f（z） - a（z）, f（z ＋ c） - a（z）, △cn f（z） - b（z） share 0 CM, then f（z ＋ c） ≡ f（z）.
文摘As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimates for weighted approximation of functions with singularities by Bernstein operators. The main results are the Jackson＇s estimates of functions f∈ （Wwλ）2 andre Cw, which extends the result of （Della Vecchia et al., 2004）.
基金jointly supported by the NSF(No.41720104006)the Strategic Priority Research Program of the Chinese Academy of Sciences(A)(No.XDA14010303)+2 种基金the National Oil and Gas Project(Nos.2016ZX05002-005-007HZ and 2016ZX05014-001-008HZ)the Shandong Innovation Project(No.2017CXGC1602)the Qingdao Innovation Project(Nos.16-5-1-40-jch and 17CX05011)
文摘The staggered-grid finite-difference （SGFD） method has been widely used in seismic forward modeling. The precision of the forward modeling results directly affects the results of the subsequent seismic inversion and migration. Numerical dispersion is one of the problems in this method. The window function method can reduce dispersion by replacing the finite-difference operators with window operators, obtained by truncating the spatial convolution series of the pseudospectral method. Although the window operators have high precision in the low-wavenumber domain, their precision decreases rapidly in the high-wavenumber domain. We develop a least squares optimization method to enhance the precision of operators obtained by the window function method. We transform the SGFD problem into a least squares problem and find the best solution iteratively. The window operator is chosen as the initial value and the optimized domain is set by the error threshold. The conjugate gradient method is also adopted to increase the stability of the solution. Approximation error analysis and numerical simulation results suggest that the proposed method increases the precision of the window function operators and decreases the numerical dispersion.
文摘In this paper, the author gives a characterization of atomic Hardy spaces associated to Schrodinger operators by using area functions, and hence gets the dual spaces of atomic Hardy spaces.
基金Supported by the Doctoral Foundation of the Education Committee of China(20050574002)
文摘Let Hn(p)be the class of functions of the form f(z)=z p+ +∞Σ k=n akzk+p,which are analytic in the open unit disk U={z:|z|<1}.In the paper,we introduce a new subclass Bn(μ,a,c,α,p;φ)of Hn(p)and investigate its subordination relations,inclusion relations and distortion theorems.The results obtained include the related results of some authors as their special case.
文摘In this paper,We mainly discuss some subclasses of analytic functions for operators onac, and determine a representation formula and sufficient condition for the class 4;(a.p,r,E,7) and prove a sufficient and necessary condition.coefficient estimates and distortiontheorem for the subclass O;o (a,p,Y,e,9) of the class ac;(a,p,y,c,V).Furthermore,the analogues also are true for operators on Hilbert space.
文摘Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions.
文摘Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.
基金supported by National Natural Science Foundation of China (10871024, 10931001, and 10971141)the Beijing Natural Science Foundation (1092004)+1 种基金Introduces Talent Fund Projects of Tianjin Normal University (5RL067)the Key Laboratory of Mathematics and Complex System (Beijing Normal University), Ministry of Education, China
文摘In this article, we prove the boundedness of commutators generated by BochnerRiesz operators below the critical index and BMO functions on the class of radial functions in Lp（Rn） with ｜1/p-1/2｜〈（1＋2α）/（2n）.
基金Supported by the Scientific Research Fund of Sichuan Provincial Education Department(Grant No.14ZB0364)
文摘In this paper, we consider a general nonlinear integral operator Hαi, βi （ f1,..., fn ; g1,..., gn）（z）. Some results including coefficient problems, univalency condition and radius of convexity for this integral operator are given. Furthermore, we discuss the mapping properties between Hαi,βi （f1 , fn, ; g1,..., gn）（z） and subclasses of analytic functions with bounded boundary rotation. The same subjects for some corresponding classes are shown upon specializing the parameters in our main results.
基金Supported in part by the Natural Science Foundation of China under the Grant 10771221Natural Science Foundation of Beijing under the Grant 1092004
文摘In this paper, we establish two weighted integral inequalities for commutators of fractional Hardy operators with Besov-Lipschitz functions. The main result is that this kind of commutator, denoted by H^ab, is bounded from L^Pxy （R＋） to L^qxδ （R＋） with the bound explicitly worked out.
