查看更多>>摘要：There is a singular integral operators Sψ on the Fock space.F2(C),which originated from the unitarily equivalent version of the Hilbert transform on L2(R).In this paper,we give an analytic characterization of functions ψ with finite zeros such that the integral operatorSψis bounded on F2(C)using Hadamard's factorization theorem.As an application,we obtain a complete characterization for such symbol functions ψ such that the Berezin transform of Sψ is bounded while the operator Sψ is not.Also,the corresponding problem in higher dimensions is considered.
查看更多>>摘要：In this paper,we consider the exterior Dirichlet problem of Hessian equa-tionsσk(λ(D2u))=g(x)with g being a perturbation of a general positive function at infinity.The existence of the viscosity solutions with generalized asymptotic behavior at infinity is established by the Perron's method which extends the previous results for Hessian equations.By the solutions of Bernoulli ordinary differential equations,the viscosity subsolutions and supersolutions are constructed.
查看更多>>摘要：We study microscopic convexity properties of convex solutions of fully non-linear parabolic equations under a structural condition introduced by Bian-Guan.We prove weak Harnack inequalities for the eigenvalues of the spatial Hessian of solutions and obtain the monotonicity of Hessian's rank with respect to time.
查看更多>>摘要：Under some natural regularity assumptions on the exponent function,we obtain the boundedness of Marcinkiewicz integrals μ,μρs and μ*λ,ρon grand variable Herz spaces.Our results enrich and improve some previous results in the literature.
查看更多>>摘要：Let P be the classical Hardy operator on(0,∞)and Q be the adjoint operator.In this paper,we get the boundedness for P,Q and the commutators of P and Q with CMO functions on the weighted Herz spaces.
查看更多>>摘要：Let(X,d)be a cone metric space and T:X → X be a mapping.In this paper,we shall introduce the concept of strong T-stability of fixed point iteration procedures with respect to T in cone metric spaces.Also,we will investigate some meaningful results on strong T-stability of Picard iterations in cone metric spaces without the as-sumption of normality.Our main results improve and generalize some related results in the literature.
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