In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.
The primary goal of this paper is to develop methods for investigating equivalent norms and HardyLittlewood-type theorems on Lipschitz-type spaces of analytic and complex-valued harmonic functions. First,we provide ch...The primary goal of this paper is to develop methods for investigating equivalent norms and HardyLittlewood-type theorems on Lipschitz-type spaces of analytic and complex-valued harmonic functions. First,we provide characterizations of equivalent norms on these spaces. Furthermore, we establish Hardy-Littlewoodtype theorems for complex-valued harmonic functions. These results improve and extend the main findings of Dyakonov(1997) and Dyakonov(2005). Additionally, we apply the derived equivalent norms and HardyLittlewood-type theorems to the study of composition operators between Lipschitz-type spaces.展开更多
It will be determined under what conditions types of proximinality are transmitted to and from quotient spaces. In the final section, by many examples we show that types of proximinality of subspaces in Banach spaces ...It will be determined under what conditions types of proximinality are transmitted to and from quotient spaces. In the final section, by many examples we show that types of proximinality of subspaces in Banach spaces can not be preserved by equivalent norms.展开更多
itherto, a precision Concept for curve fitting problems has not been set. By using the theory of functional analysis, the author of this paper established a space theory basis for curve fitting problems. Also given in...itherto, a precision Concept for curve fitting problems has not been set. By using the theory of functional analysis, the author of this paper established a space theory basis for curve fitting problems. Also given in the paper is the precision concept of the curve fitting problems and the method for constructing the fitting of a curve satisfying given precision requirements.展开更多
The Herz type Besov and Triebel-Lizorkin spaces with variable exponent are introduced. Then characterizations of these new spaces by maximal functions are given.
In this paper we consider the strongly damped and driven nonlinear wave equations under homogeneous Dirichlet boundary conditions. By introducing a new norm which is equivalent to the usual norm, we obtain the existen...In this paper we consider the strongly damped and driven nonlinear wave equations under homogeneous Dirichlet boundary conditions. By introducing a new norm which is equivalent to the usual norm, we obtain the existence of a global periodic attractor attracting any bounded set exponentially in the phase space, which implies that the system behaves exactly as a one dimensional system.展开更多
In this paper, we prove the existence of the global attractor and obtain an estimate of the upper bound of Hausdorff dimension of the attractor for strongly damped nonlinear wave equation with Dirichlet boundary condi...In this paper, we prove the existence of the global attractor and obtain an estimate of the upper bound of Hausdorff dimension of the attractor for strongly damped nonlinear wave equation with Dirichlet boundary condition by introducing a new norm. The Hausdorff dimension obtained remains small for large damping, which conforms to the physical intuition.展开更多
基金supported by the National Natural Science Foundation of China(11571104)the Hunan Provincial Innovation Foundation for Postgraduate(CX2017B220)Supported by the Construct Program of the Key Discipline in Hunan Province
文摘In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.
基金supported by National Natural Science Foundation of China (Grant No. 12071116)the Hunan Provincial Natural Science Foundation of China (Grant No. 2022JJ10001)+4 种基金the Key Projects of Hunan Provincial Department of Education (Grant No. 21A0429)the Double First-Class University Project of Hunan Province (Grant No. Xiangjiaotong [2018]469)the Science and Technology Plan Project of Hunan Province (Grant No. 2016TP1020)the Discipline Special Research Projects of Hengyang Normal University (Grant No. XKZX21002)supported by the Japan Society for the Promotion of Science KAKENHI (Grant No. JP22K03363)。
文摘The primary goal of this paper is to develop methods for investigating equivalent norms and HardyLittlewood-type theorems on Lipschitz-type spaces of analytic and complex-valued harmonic functions. First,we provide characterizations of equivalent norms on these spaces. Furthermore, we establish Hardy-Littlewoodtype theorems for complex-valued harmonic functions. These results improve and extend the main findings of Dyakonov(1997) and Dyakonov(2005). Additionally, we apply the derived equivalent norms and HardyLittlewood-type theorems to the study of composition operators between Lipschitz-type spaces.
文摘It will be determined under what conditions types of proximinality are transmitted to and from quotient spaces. In the final section, by many examples we show that types of proximinality of subspaces in Banach spaces can not be preserved by equivalent norms.
文摘itherto, a precision Concept for curve fitting problems has not been set. By using the theory of functional analysis, the author of this paper established a space theory basis for curve fitting problems. Also given in the paper is the precision concept of the curve fitting problems and the method for constructing the fitting of a curve satisfying given precision requirements.
基金This work was supported in part by the National Natural Science Foundation of China （Grant No. 11071064） and the Natural Science Foundation of Hainan Province （No. 111006）.
文摘The Herz type Besov and Triebel-Lizorkin spaces with variable exponent are introduced. Then characterizations of these new spaces by maximal functions are given.
基金Supported by the National Natural Science Foundation of China(No.10471086)
文摘In this paper we consider the strongly damped and driven nonlinear wave equations under homogeneous Dirichlet boundary conditions. By introducing a new norm which is equivalent to the usual norm, we obtain the existence of a global periodic attractor attracting any bounded set exponentially in the phase space, which implies that the system behaves exactly as a one dimensional system.
文摘In this paper, we prove the existence of the global attractor and obtain an estimate of the upper bound of Hausdorff dimension of the attractor for strongly damped nonlinear wave equation with Dirichlet boundary condition by introducing a new norm. The Hausdorff dimension obtained remains small for large damping, which conforms to the physical intuition.
