In this paper we study the convergence nf a class of means on H^p(G)(0<p<1),the means take the Bochner-Riesz means in[1],the generalized Bochner-Riesz means in[2],and the operators T^(Φ_r)in[3]as special cases....In this paper we study the convergence nf a class of means on H^p(G)(0<p<1),the means take the Bochner-Riesz means in[1],the generalized Bochner-Riesz means in[2],and the operators T^(Φ_r)in[3]as special cases.We obtain weak-type estimates for the associated maximal operators and the maximal mean boundedness for the means.展开更多
The purpose of the present paper is to evaluate the error of the approximation of the func- tion fL_1[0,1]by Kantorovich-Bernstein polynomials in L_p-metric(0<p<1).
It is well known that if f(z) belongs to Hardy space H^P in the upper plane, where 1≤p≤∞, then f(x+iy) is the Poisson integral of the corresponding boundary function on real axis. And the Paley-Wiener theorem was p...It is well known that if f(z) belongs to Hardy space H^P in the upper plane, where 1≤p≤∞, then f(x+iy) is the Poisson integral of the corresponding boundary function on real axis. And the Paley-Wiener theorem was proved for 1≤p≤2. The situation becomes different in the ease 0<p<1, since the Poisson integral formula is not established when the boundary value is taken by a function of L^P (0<p<1), which is defined almost everywhere on real axis. The classical argument of the proof of Paley-Wiener theorem does not seem quite appli-展开更多
Let D={z∈: |z|【1} and φ be a normal function on [0, 1). For p∈(0, 1) such a function φ is used to define a Bergman space A^p(φ) on D with weight φ~p(|·|)/(1-|·|~2). In this paper, the dual space of A...Let D={z∈: |z|【1} and φ be a normal function on [0, 1). For p∈(0, 1) such a function φ is used to define a Bergman space A^p(φ) on D with weight φ~p(|·|)/(1-|·|~2). In this paper, the dual space of A^p(φ) is given, four characteristics of Carleson measure on A^p(φ) are obtained. Moreover, as an application, three sequence interpolation theorems in A^p(φ) are derived.展开更多
We investigate Besov spaces and their connection with trigonometric polynomial approximation in L_p[－π,π], algebraic polynomial approximation in L_p[-1,1], algebraic polynomial approximation in L_p(S), and entir...We investigate Besov spaces and their connection with trigonometric polynomial approximation in L_p[－π,π], algebraic polynomial approximation in L_p[-1,1], algebraic polynomial approximation in L_p(S), and entire function of exponential type approximation in Lp(R), and characterize K-functionals for certain pairs of function spaces including (Lp [-π,π], B_s~α (Lp[-π，π])), (L_p(R),B_s~α (Lp(R))), (Lp[-1,1],B_s~α (Lp[-1,1])), and (Lp(S),B_s~α (Lp(S))), where 0<s<, 0<p<1, S is a simple polytope and 0<α<r.展开更多
文摘In this paper we study the convergence nf a class of means on H^p(G)(0<p<1),the means take the Bochner-Riesz means in[1],the generalized Bochner-Riesz means in[2],and the operators T^(Φ_r)in[3]as special cases.We obtain weak-type estimates for the associated maximal operators and the maximal mean boundedness for the means.
文摘The purpose of the present paper is to evaluate the error of the approximation of the func- tion fL_1[0,1]by Kantorovich-Bernstein polynomials in L_p-metric(0<p<1).
文摘It is well known that if f(z) belongs to Hardy space H^P in the upper plane, where 1≤p≤∞, then f(x+iy) is the Poisson integral of the corresponding boundary function on real axis. And the Paley-Wiener theorem was proved for 1≤p≤2. The situation becomes different in the ease 0<p<1, since the Poisson integral formula is not established when the boundary value is taken by a function of L^P (0<p<1), which is defined almost everywhere on real axis. The classical argument of the proof of Paley-Wiener theorem does not seem quite appli-
基金Supported by the Doctoral Program Foundation of Institute of Higher Education, P.R. China.
文摘Let D={z∈: |z|【1} and φ be a normal function on [0, 1). For p∈(0, 1) such a function φ is used to define a Bergman space A^p(φ) on D with weight φ~p(|·|)/(1-|·|~2). In this paper, the dual space of A^p(φ) is given, four characteristics of Carleson measure on A^p(φ) are obtained. Moreover, as an application, three sequence interpolation theorems in A^p(φ) are derived.
基金This project is supported by the National Natural Science Foundation of China.
文摘We investigate Besov spaces and their connection with trigonometric polynomial approximation in L_p[－π,π], algebraic polynomial approximation in L_p[-1,1], algebraic polynomial approximation in L_p(S), and entire function of exponential type approximation in Lp(R), and characterize K-functionals for certain pairs of function spaces including (Lp [-π,π], B_s~α (Lp[-π，π])), (L_p(R),B_s~α (Lp(R))), (Lp[-1,1],B_s~α (Lp[-1,1])), and (Lp(S),B_s~α (Lp(S))), where 0<s<, 0<p<1, S is a simple polytope and 0<α<r.
