ON WEIGHTED L^p INTEGRABILITY AND APPROXIMATION OF TRIGONOMETRIC SERIES
被引量：1
ON WEIGHTED L^p INTEGRABILITY AND APPROXIMATION OF TRIGONOMETRIC SERIES
摘要
We generalize several classical results on the integrability of trigonometric series and relations among the best approximation and the coefficients of trigonometric series. Theorem 3 and Theorem 4 are the first results on the relations among the weighted best approximation and the coefficients of trigonometric series.
We generalize several classical results on the integrability of trigonometric series and relations among the best approximation and the coefficients of trigonometric series. Theorem 3 and Theorem 4 are the first results on the relations among the weighted best approximation and the coefficients of trigonometric series.
基金
Supported in part by Hangzhou Normal University
参考文献10
-
1Yu. S. Tikhonov.On the Integrability of Trigonometric Series[].Mathematical Notes.2005
-
2Yu, D. S,Zhou, P,Zhou, S. P.On Lp?integrability and Convergence of Trigonometric Series[].Studia Mathematica.2007
-
3Yu, D. S,Zhou, S. P.On relations Among Fourier Coefficients and Sum-functions[].Studia Scientiarum Mathematicarum Hungarica.2008
-
4Yu, D. S,Zhou, S. P.The Sufficient and Necessary Condition for Trigonometric Series Belong to Ba Spaces[].Acta Mathematica Scientia.
-
5Zhou, S. P,Le, R. J.A Remark on "Two-sided" Monotonicity Condition: An Application to Lp Convergen[].Acta Mathematica Hungarica.2006
-
6Chaundy, T. W.,and Jolliffe, A. E.The Uniform Convergence of a Certain Class of Trigonometric Series[].Proc London Math Soc.1916
-
7Konyushkov,A. A.Best approximation by trigonometric polynomials and Fourier coefficients (Russian)[].Mathematics of the USSR Sbornik.1958
-
8Le, R. J.,and Zhou, S. P.A New Condition for the Uniform Convergence of Certain Trigonometric Series[].Acta Math Hungar.2005
-
9Leindler,L.Generation of inequalities of Hardy and Littlewood[].Acta Scientiarum Mathematicarum.1970
-
10Leindler,L.On the Uniform Convergence and Boundedness of a Certain Class of Sine Series[].Anal Math.2001
-
1Roman Taberski(A. Mickiewicz University, Poland).ON THE λ-MEANS OF SOME TRIGONOMETRIC SERIES[J].Analysis in Theory and Applications,1999,15(1):38-49.
-
2杨义群.ON ASYMPTOTIC BEHAVIOR OF A KIND OF TRIGONOMETRIC SERIES[J].Chinese Science Bulletin,1982,27(10).
-
3J.Kaur,S.S.Bhatia.INTEGRABILITY AND L^1-CONVERGENCE OF DOUBLE COSINE TRIGONOMETRIC SERIES[J].Analysis in Theory and Applications,2011,27(1):32-39.
-
4Chincheng Lin(Central University,Taiwan)Weichi Yang (Radford University,U.S.A).COMPARISONS OF ABSOLUTELY CONVERGENT TRIGONOMETRIC SERIES[J].Analysis in Theory and Applications,1996,12(1):116-117.
-
5Lei FENG,Vilmos TOTIK,Song Ping ZHOU.Trigonometric Series with a Generalized Monotonicity Condition[J].Acta Mathematica Sinica,English Series,2014,30(8):1289-1296. 被引量：3
-
6ZHOU SongPing,FENG FenJun,ZHANG LiJun.Trigonometric series with piecewise mean value bounded variation coefficients[J].Science China Mathematics,2013,56(8):1661-1677. 被引量：1
-
7钱伟长.SUMMATION OF TRIGONOMETRIC SERIES BY FOURIER TRANSFORMS[J].Applied Mathematics and Mechanics(English Edition),1989,10(5):385-397.
-
8Ruijun Le,Songping Zhou.A NEW CONDITION FOR CERTAIN TRIGONOMETRIC SERIES[J].Analysis in Theory and Applications,2006,22(1):1-7. 被引量：2
-
9WEI Bao-rong.L^p integrability of trigonometric series with special varying coefficients[J].Applied Mathematics(A Journal of Chinese Universities),2009,24(4):402-410.
-
10Yao Chen ZHU Academy of Mathematics and System Sciences. The Chinese Academy of Sciences, Beijing 100080. P. R. China.Transcendence of Certain Trigonometric Series[J].Acta Mathematica Sinica,English Series,2002,18(3):481-488. 被引量：2
