Let H（B） be the set of all harmonic functions f on the unit ball B of Rn. For 0 p, q ≤ ∞ and a normal weight φ, the mixed norm space Hp,q, φ（B） consists of all functions f in H（B） for which the mixed norm p,...Let H（B） be the set of all harmonic functions f on the unit ball B of Rn. For 0 p, q ≤ ∞ and a normal weight φ, the mixed norm space Hp,q, φ（B） consists of all functions f in H（B） for which the mixed norm p,q, φ ∞. In this article, we obtain some characterizations in terms of radial, tangential, and partial derivative norms in Hp,q, φ（B）. The parallel results for the Bloch-type space are also obtained. As an application, the analogous problems for polyharmonic functions are discussed.展开更多
The boundedness and compactness of the weighted differentiation composition operators from mixed-norm spaces to Bloch-type spaces are discussed in this paper.
In this paper,we prove the boundedness of the singular integral operators on product spaces with mixed norms and obtain the endpoint weak-type estimates.
Let F be a C^∞ curve in IR^n and μ be the measure induced by Lebesgue measure on F, multiplied by a smooth cut-off function. In this paper, we will prove some mixednorm estimates based on the average decay estimates...Let F be a C^∞ curve in IR^n and μ be the measure induced by Lebesgue measure on F, multiplied by a smooth cut-off function. In this paper, we will prove some mixednorm estimates based on the average decay estimates of the Fourier transform of μ.展开更多
Let {Xn,n ≥ 1} be a sequence of identically distributed ρ^--mixing random variables and set Sn =∑i^n=1 Xi,n ≥ 1,the suffcient and necessary conditions for the existence of moments of supn≥1 ｜Sn/n^1/r｜^p（0 〈 r...Let {Xn,n ≥ 1} be a sequence of identically distributed ρ^--mixing random variables and set Sn =∑i^n=1 Xi,n ≥ 1,the suffcient and necessary conditions for the existence of moments of supn≥1 ｜Sn/n^1/r｜^p（0 〈 r 〈 2,p 〉 0） are given,which are the same as that in the independent case.展开更多
Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation： f（kx ＋ y） ＋ f（kx - y） = kf（x ＋ y） ＋ kf（x - y） ＋ 2f（kx） - 2kf（x） in Banach mod...Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation： f（kx ＋ y） ＋ f（kx - y） = kf（x ＋ y） ＋ kf（x - y） ＋ 2f（kx） - 2kf（x） in Banach modules over a unital Banach algebra.展开更多
In this paper, we obtain the moment conditions for the supermun of normed sums of ρ^--mixing random variables by using the Rosenthal-type inequality for Maximum partial sums of ρ^--mixing random variables. The resul...In this paper, we obtain the moment conditions for the supermun of normed sums of ρ^--mixing random variables by using the Rosenthal-type inequality for Maximum partial sums of ρ^--mixing random variables. The result obtained generalize the results of Chen(2008) and extend those to negatively associated sequences and ρ^--mixing random variables.展开更多
The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The p...The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The pressure equation is a nonlinear parabolic equation, the concentration is defined by a convection-diffusion equation and the saturations of different components are stated by nonlinear convection-diffusion equations. The transport pressure appears in the concentration equation and saturation equations in the form of Darcy velocity, and controls their processes. The flow equation is solved by the conservative mixed volume element and the accuracy is improved one order for approximating Darcy velocity. The method of characteristic mixed volume element is applied to solve the concentration, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computational stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. The scheme can adopt a large step while its numerical results have small time-truncation error and high order of accuracy. The mixed volume element method has the law of conservation on every element for the diffusion and it can obtain numerical solutions of the concentration and adjoint vectors. It is most important in numerical simulation to ensure the physical conservative nature. The saturation different components are obtained by the method of characteristic fractional step difference. The computational work is shortened greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and it is completed easily by using the algorithm of speedup. Using the theory and technique of a priori estimates of differential equations, we derive an optimal second order estimates in 12 norm. Numerical examples are given to show the effectiveness and practicability and the method is testified as a powerful tool to solve the important problems.展开更多
The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not...The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.展开更多
This paper is concerned with a stabilized approach to low-order mixed finite element methods for the Stokes equations.We will provide a posteriori error analysis for the method.We present two a posteriori error indica...This paper is concerned with a stabilized approach to low-order mixed finite element methods for the Stokes equations.We will provide a posteriori error analysis for the method.We present two a posteriori error indicators which will be demonstrated to be globally upper and locally lower bounds for the error of the finite element discretization.Finally two numerical experiments will be carried out to show the efficiency on constructing adaptive meshes.展开更多
The authors investigate the conditions for the boundedness of Bergman type operators Ps,t in mixed norm space L_(p),q(φ)on the unit ball of C^(n)(n≥1),and obtain a sufficient condition and a necessary condition for ...The authors investigate the conditions for the boundedness of Bergman type operators Ps,t in mixed norm space L_(p),q(φ)on the unit ball of C^(n)(n≥1),and obtain a sufficient condition and a necessary condition for general normal functionφ,and a sufficient and necessary condition forφ(r)=(1-r 2)αlogβ(2(1-r)-1)(α>0,β≥0).This generalizes the result of Forelli Rudin on Bergman operator in Bergman space.As applications,a more natural method is given to compute the duality of the mixed norm space,solve the Gleason's problem for mixed norm space and obtain the characterization of mixed norm space in terms of partial derivatives.Moreover,it is proved thatf∈L(0)∞,q(φ)iff all the functions(1-|z|2)|α||α|fzα(z)∈L(0)∞,q(φ)for holomorphic functionf,1≤q≤∞.展开更多
Let Ω be a bounded convex domain with C2 boundary in C2 and for given 0 < p, q ≤∞ and normal weight function (r) let Hp,q, be the mixed norm space on Ω. In this paper we prove that the Gleason's problem (Ω...Let Ω be a bounded convex domain with C2 boundary in C2 and for given 0 < p, q ≤∞ and normal weight function (r) let Hp,q, be the mixed norm space on Ω. In this paper we prove that the Gleason's problem (Ω, a, Hp,q,) is solvable for any fixed point a ∈ Ω. While solving the Gleason's problem we obtain the boundedness of certain integral operator on Hp,q,.展开更多
In the paper, we characterize the coefficient multiplier spaces of mixed norm spaces (Hp,q((?)1),Hu,v((?)2)) for the values of p, q, u, v in three cases: (i)0<p≤u≤∞, 0 < q≤min(1,v)≤frr. (ii) v =∞,0<p≤...In the paper, we characterize the coefficient multiplier spaces of mixed norm spaces (Hp,q((?)1),Hu,v((?)2)) for the values of p, q, u, v in three cases: (i)0<p≤u≤∞, 0 < q≤min(1,v)≤frr. (ii) v =∞,0<p≤u≤∞, 1≤u, q≤∞. (iii) 1≤v≤2≤q≤∞, and 0<p≤u≤∞or 1≤p, u≤∞. The first case extends the result of Blasco, Jevtic, and Pavlovic in one variable. The third case generalizes partly the results of Jevtic, Jovanovic, and Wojtaszczyk to higher dimensions.展开更多
In this paper, we characterize the boundedness and compactness of the weighted composi- tion operators from the weighted Bergman space to the standard mixed-norm space or the mixed-norm space with normal weight on the...In this paper, we characterize the boundedness and compactness of the weighted composi- tion operators from the weighted Bergman space to the standard mixed-norm space or the mixed-norm space with normal weight on the unit ball and estimate the essential norms of the weighted composition operators.展开更多
Let Ω be a bounded domain in Rnwith a smooth boundary, and let h p,q be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h p,q, with which the definition of...Let Ω be a bounded domain in Rnwith a smooth boundary, and let h p,q be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h p,q, with which the definition of Carleson type measures for h p,q is obtained. And also, the authors obtain the boundedness of the Bergman projection on h p,q which turns out the dual space of h p,q. As an application, the authors characterize the boundedness(and compactness) of Toeplitz operators T μ on h p,q for those positive finite Borel measures μ.展开更多
基金Supported by the NNSF of China (10771064,10971063)the NSF of Zhejiang Province (Y6100219, Y7080197, Y6090036, D7080080)the Innovation Team Foundation of the Department of Education of Zhejiang Province (T200924)
文摘Let H（B） be the set of all harmonic functions f on the unit ball B of Rn. For 0 p, q ≤ ∞ and a normal weight φ, the mixed norm space Hp,q, φ（B） consists of all functions f in H（B） for which the mixed norm p,q, φ ∞. In this article, we obtain some characterizations in terms of radial, tangential, and partial derivative norms in Hp,q, φ（B）. The parallel results for the Bloch-type space are also obtained. As an application, the analogous problems for polyharmonic functions are discussed.
基金item： Supported by the National Natural Science Foundation of China（60573040）
文摘The boundedness and compactness of the weighted differentiation composition operators from mixed-norm spaces to Bloch-type spaces are discussed in this paper.
文摘In this paper,we prove the boundedness of the singular integral operators on product spaces with mixed norms and obtain the endpoint weak-type estimates.
基金Supported by Natural Science Fundation of Anhui Province (07021019)Education Committee of AnhuiProvince (KJ2007A009 KJ2008B244)
文摘Let F be a C^∞ curve in IR^n and μ be the measure induced by Lebesgue measure on F, multiplied by a smooth cut-off function. In this paper, we will prove some mixednorm estimates based on the average decay estimates of the Fourier transform of μ.
基金Supported by the National Natural Science Foundation of China (60874004)
文摘Let {Xn,n ≥ 1} be a sequence of identically distributed ρ^--mixing random variables and set Sn =∑i^n=1 Xi,n ≥ 1,the suffcient and necessary conditions for the existence of moments of supn≥1 ｜Sn/n^1/r｜^p（0 〈 r 〈 2,p 〉 0） are given,which are the same as that in the independent case.
基金supported by the National Natural Science Foundation of China (10671013,60972089,11171022)
文摘Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation： f（kx ＋ y） ＋ f（kx - y） = kf（x ＋ y） ＋ kf（x - y） ＋ 2f（kx） - 2kf（x） in Banach modules over a unital Banach algebra.
基金Supported by the National Science Foundation of China(10661006)Supported by Innovation Project of Guangxi Graduate Education(2007105960812M18)
文摘In this paper, we obtain the moment conditions for the supermun of normed sums of ρ^--mixing random variables by using the Rosenthal-type inequality for Maximum partial sums of ρ^--mixing random variables. The result obtained generalize the results of Chen(2008) and extend those to negatively associated sequences and ρ^--mixing random variables.
基金Supported by the National Natural Science Foundation of China(11101124 and 11271231)Natural Science Foundation of Shandong Province(ZR2016AM08)National Tackling Key Problems Program(2011ZX05052,2011ZX05011-004)
文摘The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The pressure equation is a nonlinear parabolic equation, the concentration is defined by a convection-diffusion equation and the saturations of different components are stated by nonlinear convection-diffusion equations. The transport pressure appears in the concentration equation and saturation equations in the form of Darcy velocity, and controls their processes. The flow equation is solved by the conservative mixed volume element and the accuracy is improved one order for approximating Darcy velocity. The method of characteristic mixed volume element is applied to solve the concentration, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computational stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. The scheme can adopt a large step while its numerical results have small time-truncation error and high order of accuracy. The mixed volume element method has the law of conservation on every element for the diffusion and it can obtain numerical solutions of the concentration and adjoint vectors. It is most important in numerical simulation to ensure the physical conservative nature. The saturation different components are obtained by the method of characteristic fractional step difference. The computational work is shortened greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and it is completed easily by using the algorithm of speedup. Using the theory and technique of a priori estimates of differential equations, we derive an optimal second order estimates in 12 norm. Numerical examples are given to show the effectiveness and practicability and the method is testified as a powerful tool to solve the important problems.
基金supported by the National Basic Research Program of China (2005CB321701)NSF of mathematics research special fund of Hebei Province(08M005)
文摘The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.
基金supported by the NSF of China(No.10971166)the National Basic Research Program(No.2005CB321703).
文摘This paper is concerned with a stabilized approach to low-order mixed finite element methods for the Stokes equations.We will provide a posteriori error analysis for the method.We present two a posteriori error indicators which will be demonstrated to be globally upper and locally lower bounds for the error of the finite element discretization.Finally two numerical experiments will be carried out to show the efficiency on constructing adaptive meshes.
文摘The authors investigate the conditions for the boundedness of Bergman type operators Ps,t in mixed norm space L_(p),q(φ)on the unit ball of C^(n)(n≥1),and obtain a sufficient condition and a necessary condition for general normal functionφ,and a sufficient and necessary condition forφ(r)=(1-r 2)αlogβ(2(1-r)-1)(α>0,β≥0).This generalizes the result of Forelli Rudin on Bergman operator in Bergman space.As applications,a more natural method is given to compute the duality of the mixed norm space,solve the Gleason's problem for mixed norm space and obtain the characterization of mixed norm space in terms of partial derivatives.Moreover,it is proved thatf∈L(0)∞,q(φ)iff all the functions(1-|z|2)|α||α|fzα(z)∈L(0)∞,q(φ)for holomorphic functionf,1≤q≤∞.
基金supported by the 151 Projetion and the Natural Science Foundation of Zhejiang Province.
文摘Let Ω be a bounded convex domain with C2 boundary in C2 and for given 0 < p, q ≤∞ and normal weight function (r) let Hp,q, be the mixed norm space on Ω. In this paper we prove that the Gleason's problem (Ω, a, Hp,q,) is solvable for any fixed point a ∈ Ω. While solving the Gleason's problem we obtain the boundedness of certain integral operator on Hp,q,.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10471134)grants from Specialized Research Fund for the doctoral program of Higher Education(SRFDP20050358052)Program for New Century Excellent Talents in University(NCET-05-0539).
文摘In the paper, we characterize the coefficient multiplier spaces of mixed norm spaces (Hp,q((?)1),Hu,v((?)2)) for the values of p, q, u, v in three cases: (i)0<p≤u≤∞, 0 < q≤min(1,v)≤frr. (ii) v =∞,0<p≤u≤∞, 1≤u, q≤∞. (iii) 1≤v≤2≤q≤∞, and 0<p≤u≤∞or 1≤p, u≤∞. The first case extends the result of Blasco, Jevtic, and Pavlovic in one variable. The third case generalizes partly the results of Jevtic, Jovanovic, and Wojtaszczyk to higher dimensions.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10971153, 10671141)
文摘In this paper, we characterize the boundedness and compactness of the weighted composi- tion operators from the weighted Bergman space to the standard mixed-norm space or the mixed-norm space with normal weight on the unit ball and estimate the essential norms of the weighted composition operators.
基金supported by the National Natural Science Foundation of China(Nos.11101139,11271124)the Natural Science Foundation of Zhejiang Province(Nos.Y6090036,Y6100219)the Foundation of Creative Group in Universities of Zhejiang Province(No.T200924)
文摘Let Ω be a bounded domain in Rnwith a smooth boundary, and let h p,q be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h p,q, with which the definition of Carleson type measures for h p,q is obtained. And also, the authors obtain the boundedness of the Bergman projection on h p,q which turns out the dual space of h p,q. As an application, the authors characterize the boundedness(and compactness) of Toeplitz operators T μ on h p,q for those positive finite Borel measures μ.
