In this paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing sm...In this paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing small functions.As an application of the value distribution result,we study the defect relation of a nonconstant solution to the partial differential equation.In particular,we give a connection between the Picard type theorem of Milliox-Hayman and the characterization of entire solutions of a partial differential equation.展开更多
In this paper it has been systematically studied the imbedding properties o f fractional integral operators of periodic functions of several variables,and isomorphic properties of fractional intregral operators in the...In this paper it has been systematically studied the imbedding properties o f fractional integral operators of periodic functions of several variables,and isomorphic properties of fractional intregral operators in the spaces of Lipschitz continuous functions. It has also been proved that the space of fractional integration,the space of Lipschitz continuous functions and the Sobolev space are identical in L^2-norm.Results obtainedhere are not true for fractional integrals(or Riesz potentials)in R^n.展开更多
Given a continuous function f defined on the unit cube of R^n and a convex function _t,_t(0)-0,_t(x)>0,for x>0,we prove that the set of best L^(t)-approximations by monotone functions has exactly one element ft,...Given a continuous function f defined on the unit cube of R^n and a convex function _t,_t(0)-0,_t(x)>0,for x>0,we prove that the set of best L^(t)-approximations by monotone functions has exactly one element ft,which is also a continuous function.Moreover if the family of convex functions {_t}t>0 converges uniformly on compact sets to a function _0, then the best approximation f_t→f_0 uniformly,as t→0,where fo is the best approximation of f within the Orlicz space L^(0) The best approxima- tions{f_t}are obtained as well as minimizing integrals or the Luxemburg norm展开更多
In this paper, we obtain a characterization of the Paley-Wiener space with several variables, which is denoted by Bπ,p(Rn), 1≤p<∞, i.e., for 1<p<∞, Bπ,p(Rn) is isomorphic to lp(Zn), and for p=1, Bπ,1(Rn...In this paper, we obtain a characterization of the Paley-Wiener space with several variables, which is denoted by Bπ,p(Rn), 1≤p<∞, i.e., for 1<p<∞, Bπ,p(Rn) is isomorphic to lp(Zn), and for p=1, Bπ,1(Rn) is isomorphic to the discrete Hardy space with several variables, which is denoted by H(Zn).展开更多
基金partially supported by the NSFC(11271227,11271161)the PCSIRT(IRT1264)the Fundamental Research Funds of Shandong University(2017JC019)。
文摘In this paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing small functions.As an application of the value distribution result,we study the defect relation of a nonconstant solution to the partial differential equation.In particular,we give a connection between the Picard type theorem of Milliox-Hayman and the characterization of entire solutions of a partial differential equation.
文摘In this paper it has been systematically studied the imbedding properties o f fractional integral operators of periodic functions of several variables,and isomorphic properties of fractional intregral operators in the spaces of Lipschitz continuous functions. It has also been proved that the space of fractional integration,the space of Lipschitz continuous functions and the Sobolev space are identical in L^2-norm.Results obtainedhere are not true for fractional integrals(or Riesz potentials)in R^n.
文摘Given a continuous function f defined on the unit cube of R^n and a convex function _t,_t(0)-0,_t(x)>0,for x>0,we prove that the set of best L^(t)-approximations by monotone functions has exactly one element ft,which is also a continuous function.Moreover if the family of convex functions {_t}t>0 converges uniformly on compact sets to a function _0, then the best approximation f_t→f_0 uniformly,as t→0,where fo is the best approximation of f within the Orlicz space L^(0) The best approxima- tions{f_t}are obtained as well as minimizing integrals or the Luxemburg norm
基金the National Natural Science Foundation of China (19671012) Doctoral Programme institution of Higher Education Foundation
文摘In this paper, we obtain a characterization of the Paley-Wiener space with several variables, which is denoted by Bπ,p(Rn), 1≤p<∞, i.e., for 1<p<∞, Bπ,p(Rn) is isomorphic to lp(Zn), and for p=1, Bπ,1(Rn) is isomorphic to the discrete Hardy space with several variables, which is denoted by H(Zn).
