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61.
In this paper, continuity of the set-valued metric generalized inverse T∂ in approximatively compact Banach spaces is investigated by means of the methods of geometry of Banach spaces. Necessary and sufficient conditions for upper semicontinuity (continuity) for the set-valued metric generalized inverses T∂ are given. Moreover, authors also prove that if X is a nearly dentable space and H is a hyperplane of X, then H is approximatively compact iff PH(x) is compact for any x∈X. 相似文献
62.
We characterize boundedness, compactness and weak compactness of Volterra operators acting between different weighted Banach spaces of entire functions with sup‐norms in terms of the symbol g; thus we complement recent work by Bassallote, Contreras, Hernández‐Mancera, Martín and Paul 3 for spaces of holomorphic functions on the disc and by Constantin and Peláez 16 for reflexive weighted Fock spaces. 相似文献
63.
64.
Existence of global bounded weak solutions to nonsymmetric systems of Keyfitz-Kranzer type 总被引:1,自引:0,他引:1
Yun-guang Lu 《Journal of Functional Analysis》2011,261(10):2797-2815
In this paper, we study the global L∞ solutions for the Cauchy problem of nonsymmetric system (1.1) of Keyfitz-Kranzer type. When n=1, (1.1) is the Aw-Rascle traffic flow model. First, we introduce a new flux approximation to obtain a lower bound ρε,δ?δ>0 for the parabolic system generated by adding “artificial viscosity” to the Aw-Rascle system. Then using the compensated compactness method with the help of L1 estimate of wε,δx(⋅,t) we prove the pointwise convergence of the viscosity solutions under the general conditions on the function P(ρ), which includes prototype function , where γ∈(−1,0)∪(0,∞), A is a constant. Second, by means of BV estimates on the Riemann invariants and the compensated compactness method, we prove the global existence of bounded entropy weak solutions for the Cauchy problem of general nonsymmetric systems (1.1). 相似文献
65.
By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms,namely we prove the existence of the weak solution. 相似文献
66.
《Expositiones Mathematicae》2019,37(1):84-91
The purpose of this short note is to provide a new and very short proof of a result by Sudakov (1957), offering an important improvement of the classical result by Kolmogorov–Riesz on compact subsets of Lebesgue spaces. 相似文献
67.
Let n>1 and B be the unit ball in n dimensions complex space Cn.Suppose thatφis a holomorphic self-map of B andψ∈H(B)withψ(0)=0.A kind of integral operator,composition Cesàro operator,is defined by Tφψ(f)(z)=∫10f[φ(tz)]Rψ(tz)dt/t,f∈(B)z∈B.In this paper,the authors characterize the conditions that the composition Cesàro operator T_φ,ψis bounded or compact on the normal weight Zygmund space Z_μ(B).At the same time,the sufficient and necessary conditions for all cases are given. 相似文献
68.
69.
Shaoguang Shi & Zunwei Fu 《分析论及其应用》2021,37(3):347-361
The more explicit decomposition of the operator and the kernel are utilized to investigate a characterization of the central $BMO(\mathbb{R}^{n})$-closure of $C_{c}^{\infty}(\mathbb{R}^{n})$ space via the compactness of the commutators of fractional Hardy operator with rough kernel. 相似文献
70.
Geng Zhibin 《大学数学》1998,(2)
本文研究了Banach空间的弱序列紧性.Banach空间X称为有(w)性质,如果X(X的共轭空间)的每个有界序列有弱收敛子列.我们证明了,如果Banach空间X有(w)性质,那么lp(X)(1≤p<+∞)与c0(X)也有(w)性质. 相似文献