Q_p空间中的de la Vallée Poussin平均
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摘要
本文研究了单位球上的Q_p空间中的de la Vallée Poussin平均算子,并通过高阶光滑模来建立Jackson逼近定理.此外,我们还得到了Bernstein不等式,K-泛函和光滑模的等价刻画等结果.
In this paper, we introduce the de la Vallee Poussin means on the unit ball of C~n and establish in Q_p spaces the Jackson's approximation theorem in terms of the higher orders of modulus of smoothness, the Bernstein type inequalities, and the equivalence characterization between modulus of smoothness and K-functional.
In this paper, we introduce the de la Vallee Poussin means on the unit ball of C~n and establish in Q_p spaces the Jackson's approximation theorem in terms of the higher orders of modulus of smoothness, the Bernstein type inequalities, and the equivalence characterization between modulus of smoothness and K-functional.
引文
[1] Natanson I P. Constructive function theory[M]. Vol. 1. New York:Ungar, 1964.
[2] Pólya G, Schoenberg I J. Remarks on de la Vallee Poussin means and convex conformal maps of the circle[J]. Pacific J. Math., 1958, 8(2):295-335.
[3] DeVore R A, Lorentz G G. Construction approximation[M]. Berlin:Springer-Verlag, 1993.
[4] Butzer P L. On the singular integral of de la Vallée-Pousin[J]. Arch. Math., 1956, 7(4):295-309.
[5] Ding C, Yang R, Cao F. The strong converse inequality for de la Vallee Poussin means on the sphere[J]. J. Comput. Anal. Appl., 2016, 20(1):34-41.
[6] Gal S G, Sabadini I. Approximation by polynomials on quaternionic compact sets[J]. Math. Meth.Appl. Sci., 2015, 38(14):3063-3074.
[7] Muir J R, Suffridge T J. De la Vallee Poussin means of holomorphic mappings of the ball[A].Complex analysis and dynamical systems IV. Part 1, 231-243, Contemp. Math. 553, Providence,RI, 2011.
[8] Zhu K. Spaces of holomorphic functions in the unit ball[M]. New York:Springer, 2005.
[9] Choa J S, Choa B R. A Littlewood-Paley type identity and a characterization of BMOA[J].Complex, 1991, 17:15-23.
[10] Aulaskari R, Xiao J, Zhao R H. On subspaces and subsets of BMOA and UBC[J]. Analysis, 1995,15:101-121.
[11] Ouyang C H, Yang W S,Zhao R H. M(o|¨)bius invariant Q_p spaces associated with the Green's function on the unit ball of C~n[J]. Pacific J. Math., 1998, 182:69-99.
[12] Li B, Ouyang C H. Higher radial derivative of Bloch type functions[J]. Acta Math. Sci. Ser. B,2002, 22:433-445.
[13] Ren G B, Chen Y W. Gradient estimates and Jackson's theorem in Q_u spaces related to measures[J]. J. Approx. Theory, 2008, 155(2):97-110.
[14] Yang W. Carleson type measure characterizations of Qp spaces[J]. Analysis, 1998, 18:345-349.
[15] Xiao J. Holomorphic Q classes[M]. Berlin:Springer-Verlag, 2001.
[2] Pólya G, Schoenberg I J. Remarks on de la Vallee Poussin means and convex conformal maps of the circle[J]. Pacific J. Math., 1958, 8(2):295-335.
[3] DeVore R A, Lorentz G G. Construction approximation[M]. Berlin:Springer-Verlag, 1993.
[4] Butzer P L. On the singular integral of de la Vallée-Pousin[J]. Arch. Math., 1956, 7(4):295-309.
[5] Ding C, Yang R, Cao F. The strong converse inequality for de la Vallee Poussin means on the sphere[J]. J. Comput. Anal. Appl., 2016, 20(1):34-41.
[6] Gal S G, Sabadini I. Approximation by polynomials on quaternionic compact sets[J]. Math. Meth.Appl. Sci., 2015, 38(14):3063-3074.
[7] Muir J R, Suffridge T J. De la Vallee Poussin means of holomorphic mappings of the ball[A].Complex analysis and dynamical systems IV. Part 1, 231-243, Contemp. Math. 553, Providence,RI, 2011.
[8] Zhu K. Spaces of holomorphic functions in the unit ball[M]. New York:Springer, 2005.
[9] Choa J S, Choa B R. A Littlewood-Paley type identity and a characterization of BMOA[J].Complex, 1991, 17:15-23.
[10] Aulaskari R, Xiao J, Zhao R H. On subspaces and subsets of BMOA and UBC[J]. Analysis, 1995,15:101-121.
[11] Ouyang C H, Yang W S,Zhao R H. M(o|¨)bius invariant Q_p spaces associated with the Green's function on the unit ball of C~n[J]. Pacific J. Math., 1998, 182:69-99.
[12] Li B, Ouyang C H. Higher radial derivative of Bloch type functions[J]. Acta Math. Sci. Ser. B,2002, 22:433-445.
[13] Ren G B, Chen Y W. Gradient estimates and Jackson's theorem in Q_u spaces related to measures[J]. J. Approx. Theory, 2008, 155(2):97-110.
[14] Yang W. Carleson type measure characterizations of Qp spaces[J]. Analysis, 1998, 18:345-349.
[15] Xiao J. Holomorphic Q classes[M]. Berlin:Springer-Verlag, 2001.