The boundedness and compactness of the weighted differentiation composition operators from mixed-norm spaces to Bloch-type spaces are discussed in this paper.
The Bloch-type space Bω consists of all functions f ∈ H(B) for which||f||Bω=sup/z∈Bω(z)|▽f(z)|< ∞.Let T be the extended Ces`aro operator with holomorphic symbol . The essential norm of T as an operator f...The Bloch-type space Bω consists of all functions f ∈ H(B) for which||f||Bω=sup/z∈Bω(z)|▽f(z)|< ∞.Let T be the extended Ces`aro operator with holomorphic symbol . The essential norm of T as an operator from Bω to Bμ is denoted by ||T||e,B ω→Bμ . The purpose of this paper is to prove that, for ω, μ normal and ∈H(B)||T||e,B ω→Bμ■ lim sup|z|→1 μ(z)|■ (z)|∫ |z| 0 dt ω(t) .展开更多
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
Extending the results of an article published in(Acta Mathematica Sinica(2016,59(4)) by the author, for a sequence of normed spaces {Xi}, the representation problem of conjugate spaces of some l^0({X_i}) type F-normed...Extending the results of an article published in(Acta Mathematica Sinica(2016,59(4)) by the author, for a sequence of normed spaces {Xi}, the representation problem of conjugate spaces of some l^0({X_i}) type F-normed spaces are studied in this paper. The algebraic representation continued equalities l^0({X_i}) * A=c_(00)~0({X_i}) * A= c_(00)({X_i~*}),(l^0(X))~* A=(c^0(X) )~* A=(c_0~0(X))~* A=(c_(00)~0(X))~* A= c_(00)(X~*)are obtained in the first part. Under weak-star topology, the topological representation c_(00)~0({X_i}) ~*, w~* = c_(00)~0({X_i~*}) is obtained in the second part. For the sequence of inner product spaces and number fields with the usual topology, the concrete forms of the basic representation theorems are obtained at last.展开更多
Let C be a closed convex weakly Cauchy subset of a normed space X. Then we define a new {a,b,c} type nonexpansive and {a,b,c} type contraction mapping T from C into C. These types of mappings will be denoted respectiv...Let C be a closed convex weakly Cauchy subset of a normed space X. Then we define a new {a,b,c} type nonexpansive and {a,b,c} type contraction mapping T from C into C. These types of mappings will be denoted respectively by {a,b,c}-ntype and {a,b,c}-ctype. We proved the following： 1. If T is {a,b,c}-ntype mapping, then inf{ ｜｜ T（x）-x｜｜ ：x C C} =0, accordingly T has a unique fixed point. Moreover, any sequence {Xn}n∈NN in C with limn→∞｜｜T（xn） - Xn｜｜ = 0 has a subsequence strongly convergent to the unique fixed point of T. 2. If T is {a,b,c}-ctype mapping, then T has a unique fixed point. Moreover, for any x∈C the sequence of iterates {Tn （x）}n∈N has subsequence strongly convergent to the unique fixed point of T. This paper extends and generalizes some of the results given in [2,4, 7] and [13].展开更多
The theta (t)-type oscillatory singular integral operators has been discussed. With the non-negative locally integrable weighted function, the weighted norm inequality of theta ( t) -type oscillatory singular integral...The theta (t)-type oscillatory singular integral operators has been discussed. With the non-negative locally integrable weighted function, the weighted norm inequality of theta ( t) -type oscillatory singular integral operators is proved, and the weighted function has replaced by action of Hardy-Littlewood maximal operators several times.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
The local robust stabilization for a class of nonlinear uncertain systems is studied. The robustness concept of Lyapunov type stabilizability for nonlinear uncertain systems is defined. Under the norm bounded struct...The local robust stabilization for a class of nonlinear uncertain systems is studied. The robustness concept of Lyapunov type stabilizability for nonlinear uncertain systems is defined. Under the norm bounded structured condition, two cases for uncertainty in control matrix are taken to discuss Lyapunov type stabilizability of systems. The sufficient conditions of Lyapunov type stabilization are given from differential geometry and nonlinear H ∞ control of view, respectively.展开更多
The purpose of this paper is to introduce the coneept of (Φ,△)-type probabilistic contractor in Menger PN-spaces and to study the existence and uniqueness of solutions for the nonlinear operator equations with such ...The purpose of this paper is to introduce the coneept of (Φ,△)-type probabilistic contractor in Menger PN-spaces and to study the existence and uniqueness of solutions for the nonlinear operator equations with such probabilistic contractor in Menger PN-spaces.The results presented in this paper improve and extend the corresponding results in [1] and [4-8].展开更多
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.
基金Supported by the NNSF of China（10771064） Supported by the Natural Science Foundation of Zhejiang Province（YT080197, Y6090036, Y6100219） Supported by the Foundation of Creative Group in Colleges and Universities of Zhejiang Province（T200924）
Acknowledgement The author would like to express her thanks to her supervisor, Prof HU Zhang-jian, for his guidance.
文摘The Bloch-type space Bω consists of all functions f ∈ H(B) for which||f||Bω=sup/z∈Bω(z)|▽f(z)|< ∞.Let T be the extended Ces`aro operator with holomorphic symbol . The essential norm of T as an operator from Bω to Bμ is denoted by ||T||e,B ω→Bμ . The purpose of this paper is to prove that, for ω, μ normal and ∈H(B)||T||e,B ω→Bμ■ lim sup|z|→1 μ(z)|■ (z)|∫ |z| 0 dt ω(t) .
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Supported by the National Natural Science Foundation of China（11471236）
文摘Extending the results of an article published in(Acta Mathematica Sinica(2016,59(4)) by the author, for a sequence of normed spaces {Xi}, the representation problem of conjugate spaces of some l^0({X_i}) type F-normed spaces are studied in this paper. The algebraic representation continued equalities l^0({X_i}) * A=c_(00)~0({X_i}) * A= c_(00)({X_i~*}),(l^0(X))~* A=(c^0(X) )~* A=(c_0~0(X))~* A=(c_(00)~0(X))~* A= c_(00)(X~*)are obtained in the first part. Under weak-star topology, the topological representation c_(00)~0({X_i}) ~*, w~* = c_(00)~0({X_i~*}) is obtained in the second part. For the sequence of inner product spaces and number fields with the usual topology, the concrete forms of the basic representation theorems are obtained at last.
文摘Let C be a closed convex weakly Cauchy subset of a normed space X. Then we define a new {a,b,c} type nonexpansive and {a,b,c} type contraction mapping T from C into C. These types of mappings will be denoted respectively by {a,b,c}-ntype and {a,b,c}-ctype. We proved the following： 1. If T is {a,b,c}-ntype mapping, then inf{ ｜｜ T（x）-x｜｜ ：x C C} =0, accordingly T has a unique fixed point. Moreover, any sequence {Xn}n∈NN in C with limn→∞｜｜T（xn） - Xn｜｜ = 0 has a subsequence strongly convergent to the unique fixed point of T. 2. If T is {a,b,c}-ctype mapping, then T has a unique fixed point. Moreover, for any x∈C the sequence of iterates {Tn （x）}n∈N has subsequence strongly convergent to the unique fixed point of T. This paper extends and generalizes some of the results given in [2,4, 7] and [13].
基金Supported by Natural Science Foundation of Xinjiang Uygur Autonomous Region(2021D01B35)Natural Science Foundation of colleges and universities in Xinjiang Uygur Au-tonomous Region(XJEDU2021Y048)Doctoral Initiation Fund of Xinjiang Institute of Engineering(2020xgy012302).
基金Foundation item:the Education Commission of Shandong Province(J98P51)
文摘The theta (t)-type oscillatory singular integral operators has been discussed. With the non-negative locally integrable weighted function, the weighted norm inequality of theta ( t) -type oscillatory singular integral operators is proved, and the weighted function has replaced by action of Hardy-Littlewood maximal operators several times.
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The local robust stabilization for a class of nonlinear uncertain systems is studied. The robustness concept of Lyapunov type stabilizability for nonlinear uncertain systems is defined. Under the norm bounded structured condition, two cases for uncertainty in control matrix are taken to discuss Lyapunov type stabilizability of systems. The sufficient conditions of Lyapunov type stabilization are given from differential geometry and nonlinear H ∞ control of view, respectively.
文摘The purpose of this paper is to introduce the coneept of (Φ,△)-type probabilistic contractor in Menger PN-spaces and to study the existence and uniqueness of solutions for the nonlinear operator equations with such probabilistic contractor in Menger PN-spaces.The results presented in this paper improve and extend the corresponding results in [1] and [4-8].
