Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting...Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.展开更多
We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the gener...We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the generators of ϕ<sup>j</sup>-bounded strongly continuous semigroups. Furthermore, these results are used to investigate the effect of the Perturbation on the type of the growth of sequences.展开更多
In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit...In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit ball of X.We next give a sharp result on the first order Fréchet derivative for bounded holomorphic mappings F(X)=F(0+)∞∑s=KD^(s)f(0)(x^(8)/s!):B_(X)→B_(Y),where B_(X)is the unit ball of X.The results that we derive include some results in several complex variables,and extend the classical result in one complex variable to several complex variables.展开更多
In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order t...In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.展开更多
The main topic in this note is to discuss the boundedness of pseudo-differential operators and para-product nptfators on ihe Holder and Sobotev space;, respectively It is the preparation of the thoery of Gibbs - Butze...The main topic in this note is to discuss the boundedness of pseudo-differential operators and para-product nptfators on ihe Holder and Sobotev space;, respectively It is the preparation of the thoery of Gibbs - Butzer deffereftital operators and differential equations.展开更多
It is well known that, the singular integral operatorS defined as: ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH μ(L) intoH μ(L): ifL is an open smooth curve, thenS...It is well known that, the singular integral operatorS defined as: ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH μ(L) intoH μ(L): ifL is an open smooth curve, thenS is just a linear operator fromH * intoH *. In this paper, we define a Banach space , and prove that is a bounded linear operator, then verify the boundedness of other kinds of singular integral operators.展开更多
The thermistor problem is a coupled system of nonlinear PDEs with mixed boundary conditions. The goal of this paper is to study the existence, boundedness and uniqueness of the weak solution for this problem.
This article considers the following higher-dimensional quasilinear parabolic-parabolic-ODE chemotaxis system with generalized Logistic source and homogeneous Neumann boundary conditions{ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+f(u),...This article considers the following higher-dimensional quasilinear parabolic-parabolic-ODE chemotaxis system with generalized Logistic source and homogeneous Neumann boundary conditions{ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+f(u),x∈Ω,t>0 vt=Δv+w−v,x∈Ω,t>0,wt=u−w,x∈Ω,t>0,in a bounded domainΩ⊂R^n(n≥2)with smooth boundary ∂Ω,where the diffusion coefficient D(u)and the chemotactic sensitivity function S(u)are supposed to satisfy D(u)≥M1(u+1)^−αand S(u)≤M2(u+1)^β,respectively,where M1,M2>0 and α,β∈R.Moreover,the logistic source f(u)is supposed to satisfy f(u)≤a−μu^γ with μ>0,γ≥1,and a≥0.Asα+2β<γ−1+2γ/n,we show that the solution of the above chemotaxis system with sufficiently smooth nonnegative initial data is uniformly bounded.展开更多
In this article, the author studies the boundedness and convergence for the non-Liénard type differential equation {^·x=a（y）-f（x）,^·y=b（y）β（x）-g（x）＋e（t）,where a（y）, b（y）, f（x）, g（x...In this article, the author studies the boundedness and convergence for the non-Liénard type differential equation {^·x=a（y）-f（x）,^·y=b（y）β（x）-g（x）＋e（t）,where a（y）, b（y）, f（x）, g（x）,β（x） are real continuous functions in y ∈ R or x ∈ R, β（x） ≥ 0 for all x and e（t） is a real continuous function on R^＋ = {t ： t ≥ 0} such that the equation has a unique solution for the initial value problem. The necessary and sufficient conditions are obtained and some of the results in the literatures are improved and extended.展开更多
In this paper, some results concerning the relationship between the bounded-ness of some spheres and the local boundedness of the .F*-space are presented. Moreover, some results about the compactness are also given.
This paper investigates equation (1) in twocases:(i)P=0, (ii)P satisfies|P (i,x,y,z,w)<(A+|y|+|z|+|w|)q(t).whereq(t) is a nonnegative function of t. For case (i) the asymptotic stability in the large of the trivial...This paper investigates equation (1) in twocases:(i)P=0, (ii)P satisfies|P (i,x,y,z,w)<(A+|y|+|z|+|w|)q(t).whereq(t) is a nonnegative function of t. For case (i) the asymptotic stability in the large of the trivial solution x=0 is investigated and for case (ii) the boundedness result is obtained for solutions of equation (1). These results improve and include several well-known results.展开更多
In this paper, we first present constructing a Lyapunov function for (1. 1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p≡ 0,and the boundedness result of the sol...In this paper, we first present constructing a Lyapunov function for (1. 1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p≡ 0,and the boundedness result of the solutions of (1 .1 ) for case p≠0. These results improve sveral well-known results.展开更多
In this paper, we study certain non-autonomous third order delay differential equations with continuous deviating argument and established sufficient conditions for the stability and boundedness of solutions of the eq...In this paper, we study certain non-autonomous third order delay differential equations with continuous deviating argument and established sufficient conditions for the stability and boundedness of solutions of the equations. The conditions stated complement previously known results. Example is also given to illustrate the correctness and significance of the result obtained.展开更多
Lp(Rn) boundedness is considered for the higher-dimensional Marcinkiewicz integral which was introduced by Stein. Some conditions implying the Lp(Rn) boundedness for the Marcinkiewicz integral are obtained.
After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. ...After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:展开更多
For denote the Lebesgue space for and the Hardy space for p <1 In this paper, the authors study mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or ...For denote the Lebesgue space for and the Hardy space for p <1 In this paper, the authors study mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or the standard fractional integral with the Calderon-Zygmund operator. The authors prove that such mapping properties hold if and only if these operators satisfy certain cancellation conditions.展开更多
There are given sufficient conditions for the ultimate boundedness of solutions and for the existence of periodic solutions of a certain vector differential equation of third-order.
It provides the boundary proof of the maximal operator on Lipschitz space. i.e.,if f ∈Lip α(R n) (0<α<1) and inf x∈R nM(f)(x) <∞, then almost every x∈R n has M(f)(x) <∞ and exists a constant C indep...It provides the boundary proof of the maximal operator on Lipschitz space. i.e.,if f ∈Lip α(R n) (0<α<1) and inf x∈R nM(f)(x) <∞, then almost every x∈R n has M(f)(x) <∞ and exists a constant C independent of f and x ,such that ‖M(f)‖ ∧ α ≤C‖f‖ ∧ α .展开更多
文摘Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.
文摘We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the generators of ϕ<sup>j</sup>-bounded strongly continuous semigroups. Furthermore, these results are used to investigate the effect of the Perturbation on the type of the growth of sequences.
基金supported by the NSFC(11871257,12071130)supported by the NSFC(11971165)。
文摘In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit ball of X.We next give a sharp result on the first order Fréchet derivative for bounded holomorphic mappings F(X)=F(0+)∞∑s=KD^(s)f(0)(x^(8)/s!):B_(X)→B_(Y),where B_(X)is the unit ball of X.The results that we derive include some results in several complex variables,and extend the classical result in one complex variable to several complex variables.
基金supported by the Natural Science Foundation of Hunan Province of China(2022JJ30369)the Education Department Important Foundation of Hunan Province in China(23A0095)。
文摘In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.
文摘The main topic in this note is to discuss the boundedness of pseudo-differential operators and para-product nptfators on ihe Holder and Sobotev space;, respectively It is the preparation of the thoery of Gibbs - Butzer deffereftital operators and differential equations.
文摘It is well known that, the singular integral operatorS defined as: ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH μ(L) intoH μ(L): ifL is an open smooth curve, thenS is just a linear operator fromH * intoH *. In this paper, we define a Banach space , and prove that is a bounded linear operator, then verify the boundedness of other kinds of singular integral operators.
文摘The thermistor problem is a coupled system of nonlinear PDEs with mixed boundary conditions. The goal of this paper is to study the existence, boundedness and uniqueness of the weak solution for this problem.
基金This work is supported by the Youth Doctor Science and Technology Talent Training Project of Xinjiang Uygur Autonomous Region(2017Q087).
文摘This article considers the following higher-dimensional quasilinear parabolic-parabolic-ODE chemotaxis system with generalized Logistic source and homogeneous Neumann boundary conditions{ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+f(u),x∈Ω,t>0 vt=Δv+w−v,x∈Ω,t>0,wt=u−w,x∈Ω,t>0,in a bounded domainΩ⊂R^n(n≥2)with smooth boundary ∂Ω,where the diffusion coefficient D(u)and the chemotactic sensitivity function S(u)are supposed to satisfy D(u)≥M1(u+1)^−αand S(u)≤M2(u+1)^β,respectively,where M1,M2>0 and α,β∈R.Moreover,the logistic source f(u)is supposed to satisfy f(u)≤a−μu^γ with μ>0,γ≥1,and a≥0.Asα+2β<γ−1+2γ/n,we show that the solution of the above chemotaxis system with sufficiently smooth nonnegative initial data is uniformly bounded.
基金The project is sponsored by National Science Foundation of China (10671020)
文摘In this article, the author studies the boundedness and convergence for the non-Liénard type differential equation {^·x=a（y）-f（x）,^·y=b（y）β（x）-g（x）＋e（t）,where a（y）, b（y）, f（x）, g（x）,β（x） are real continuous functions in y ∈ R or x ∈ R, β（x） ≥ 0 for all x and e（t） is a real continuous function on R^＋ = {t ： t ≥ 0} such that the equation has a unique solution for the initial value problem. The necessary and sufficient conditions are obtained and some of the results in the literatures are improved and extended.
基金This research is supported by National Natural Science Foundation of China(19971046) RFDP(2001005513)
文摘In this paper, some results concerning the relationship between the bounded-ness of some spheres and the local boundedness of the .F*-space are presented. Moreover, some results about the compactness are also given.
文摘This paper investigates equation (1) in twocases:(i)P=0, (ii)P satisfies|P (i,x,y,z,w)<(A+|y|+|z|+|w|)q(t).whereq(t) is a nonnegative function of t. For case (i) the asymptotic stability in the large of the trivial solution x=0 is investigated and for case (ii) the boundedness result is obtained for solutions of equation (1). These results improve and include several well-known results.
文摘In this paper, we first present constructing a Lyapunov function for (1. 1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p≡ 0,and the boundedness result of the solutions of (1 .1 ) for case p≠0. These results improve sveral well-known results.
文摘In this paper, we study certain non-autonomous third order delay differential equations with continuous deviating argument and established sufficient conditions for the stability and boundedness of solutions of the equations. The conditions stated complement previously known results. Example is also given to illustrate the correctness and significance of the result obtained.
基金The research was supported by the NSF of Henan Province.
文摘Lp(Rn) boundedness is considered for the higher-dimensional Marcinkiewicz integral which was introduced by Stein. Some conditions implying the Lp(Rn) boundedness for the Marcinkiewicz integral are obtained.
文摘After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:
基金Supported by the NNSF and the National Education Comittee of China
文摘For denote the Lebesgue space for and the Hardy space for p <1 In this paper, the authors study mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or the standard fractional integral with the Calderon-Zygmund operator. The authors prove that such mapping properties hold if and only if these operators satisfy certain cancellation conditions.
文摘There are given sufficient conditions for the ultimate boundedness of solutions and for the existence of periodic solutions of a certain vector differential equation of third-order.
文摘It provides the boundary proof of the maximal operator on Lipschitz space. i.e.,if f ∈Lip α(R n) (0<α<1) and inf x∈R nM(f)(x) <∞, then almost every x∈R n has M(f)(x) <∞ and exists a constant C independent of f and x ,such that ‖M(f)‖ ∧ α ≤C‖f‖ ∧ α .
