The Fejér-Riesz inequality for the Besov spaces

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Abstract

A Fejér-Riesz inequality for the weighted Besov spaces B p,q is given. Some characterizations of functions in B p,q in terms of their Taylor coefficients are obtained.

Keywords

Fejer-Riesz inequality Besov spaces Taylor coefficients 

MR(2000) Subject Classification

30D55 

References

  1. [1]
    Fejér, L., Riesz, F.: Über einige funktionentheoretische Ungleichungen. Math. Zeitschrift, 11, 305–314 (1921)CrossRefGoogle Scholar
  2. [2]
    Hardy, G., Littlewood, J., Pólya, G.: Inequalities, Cambridge Univ. Press, London-New York, 1934Google Scholar
  3. [3]
    Huber, A.: On an inequality of Fejér and Riesz. Ann. of Math., 63, 572–587 (1956)MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    Shield, A.: An analogue of the Fejér-Riesz theorem for the Dirichlet space. In: Proceedings of Conference on Harmonic Analysis in honour of Antoni Zygmund (W. Beckner et al. eds.), II, 1983, 810–820Google Scholar
  5. [5]
    Soykan, Y.: An inequality of Fejér-Riesz type. Cankaya Üniversitesi Fen-Edebiyat Fakütesi, Journal of Arts and Sciences, 5, 51–60 (2006)Google Scholar
  6. [6]
    Holland, F., Walsh, D.: Growth estimates for functions in the Besov spaces A p. Pro. Roy. Irish Acad., 88A, 1–18 (1988)MathSciNetGoogle Scholar
  7. [7]
    Mateljević, M., Pavlović, M.: L p-behaviour of power series with positive coefficients and Hardy spaces. Proc. Amer. Math. Soc., 87, 309–316 (1983)MathSciNetMATHGoogle Scholar
  8. [8]
    Duren, P.: Theory of H p Spaces, Academic Press, New York-London, 1970MATHGoogle Scholar
  9. [9]
    Zhao, R.: On a general family of function spaces. Ann. Acad. Sci. Fenn. Math. Diss, 105, 1–56 (1996)Google Scholar
  10. [10]
    Zygmund, A.: Trigonometric Series, Vol. I, Cambridge Univ. Press, New York, 1968Google Scholar

Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of MathematicsShantou UniversityShantouP. R. China

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