查看更多>>摘要：In this paper,we investigate subelliptic harmonic maps with a potential from noncompact complete sub-Riemannian manifolds corresponding to totally geodesic Rieman-nian foliations.Under some suitable conditions,we give the gradient estimates of these maps and establish a Liouville type result.
查看更多>>摘要：Let(X,T)be a linear dynamical system,where X is a Banach space and T:X →X is a bounded linear operator.This paper obtains that(X,T)is sensitive(Li-Yorke sensitive,mean sensitive,syndetically mean sensitive,respectively)if and only if(X,T)is Banach mean sensitive(Banach mean Li-Yorke sensitive,thickly multi-mean sensitive,thickly syndetically mean sensitive,respectively).Several examples are provided to distinguish between different notions of mean sensitivity,syndetic mean sensitivity and mean Li-Yorke sensitivity.
查看更多>>摘要：In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of orthogonal projections attains its optimal value.
查看更多>>摘要：Let qλ(z)=1+λsinh(ζ),0＜λ＜1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S*(qλ)of starlike functions which contains the functions f such that zf'/f is subordinated by qλ.We establish inclusion and radii results for the class S*(qλ)for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S*(qλ).We also find a sharp bound for the third Hankel determinant for the case λ=1/2.
查看更多>>摘要：Fractional calculus has drawn more attentions of mathematicians and engineer-s in recent years.A lot of new fractional operators were used to handle various practical problems.In this article,we mainly study four new fractional operators,namely the Caputo-Fabrizio operator,the Atangana-Baleanu operator,the Sun-Hao-Zhang-Baleanu operator and the generalized Caputo type operator under the frame of the k-Prabhakar fractional integral operator.Usually,the theory of the k-Prabhakar fractional integral is regarded as a much broader than classical fractional operator.Here,we firstly give a series expansion of the k-Prabhakar fractional integral by means of the k-Riemann-Liouville integral.Then,a con-nection between the k-Prabhakar fractional integral and the four new fractional operators of the above mentioned was shown,respectively.In terms of the above analysis,we can obtain this a basic fact that it only needs to consider the k-Prabhakar fractional integral to cover these results from the four new fractional operators.
查看更多>>摘要：We consider a first order periodic system in RN,involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturba-tion.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.
查看更多>>摘要：In this paper,we investigate sufficient and necessary conditions such that gen-eralized Forelli-Rudin type operators Tλ,τ,k,Sλ,T,k,Qλ,τ,k and Rλ,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.
查看更多>>摘要：For analytic functions u,ψ in the unit disk D in the complex plane and an analytic self-map φ of D,we describe in this paper the boundedness and compactness of product type operators Tu,ψ,φf(z)=u(z)f(φ(z)+ψ(z)f'(φ(z)),z ∈ D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.
查看更多>>摘要：In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞Σs=1Dskf(0)(xsk)/(sk)!:BX→BY,where Bx 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)+∞Σs=kDsf(0)(xs)/s!:BX → BY,where BX 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.
查看更多>>摘要：The Landau equation is studied for hard potential with-2 ≤ γ ≤ 1.Under a perturbation setting,a unique global solution of the Cauchy problem to the Landau equation is established in a critical Sobolev space HdxL2v(d＞3/2),which extends the results of[11]in the torus domain to the whole space R3x.Here we utilize the pseudo-differential calculus to derive our desired result.
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