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Majorized toeplitz forms and weighted inequalities with general norms

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Harmonic Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 908))

Abstract

A more general version of the lifting theorem [4] is given, which allows applications to LP and other normed spaces. Weighted inequalities and moment problems for the Hilbert and the Poisson operators and for generalized Toeplitz forms are considered for the one-dimensional periodic case.

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References

  1. V.M. Adamjan, D.Z. Arov and M.G. Krein Infinite Hankel matrices and problems of Carathéodory and Fejér, Func. Anal. Appl. 2 (1968), 1–19.

    Article  Google Scholar 

  2. R. Arocena, M. Cotlar and C. Sadosky, Weighted Inequalities in L2 and Lifting Properties, Math. Anal. & Appl., Part A, Adv. in Math. Suppl. Studies, 7A (1981), 95–128.

    MathSciNet  MATH  Google Scholar 

  3. R. Arocena and M. Cotlar, Generalized Toeplitz Kernels and moment problems of Adamjan-Arov-Krein, to appear in Integral Eq. and Operator Theory.

    Google Scholar 

  4. M. Cotlar and C. Sadosky, On the Helson-Szegö theorem and a related class of modified Toeplitz kernels, Proc. Symp. Pure Math. AMS, 25:I (1979), 383–407.

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Cotlar and C. Sadosky, Characterization of two measures satisfying the Riesz inequality for the Hilbert transform in L2, Acta Cient. Venezolana 30 (1979), 346–348.

    MathSciNet  MATH  Google Scholar 

  6. M. Cotlar and C. Sadosky, On some LP versions of the Helson-Szegö theorem, Harmonic Analysis Conference in honour of Prof. A. Zygmund, preprint.

    Google Scholar 

  7. C. Fefferman and E.M. Stein, HP spaces of several variables, Acta Math., 129 (1972), 137–193.

    Article  MathSciNet  MATH  Google Scholar 

  8. H. Helson and G. Szegö, A problem in Prediction Theory, Ann. Math. Pura Appl., 51 (1960), 107–138.

    Article  MathSciNet  MATH  Google Scholar 

  9. S. Krein, In, Petunin, E. Semionov, “Interpolation of linear operators,” Nauka, Moscow, 1978 (in Russian).

    MATH  Google Scholar 

  10. B. Muckenhoupt, Two weight function norm inequalities for the Poisson integral, Trans. Amer. Math. Soc., 210 (1975), 225–231.

    Article  MathSciNet  MATH  Google Scholar 

  11. R.R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math., 51 (1974), 241–250.

    MathSciNet  MATH  Google Scholar 

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Fulvio Ricci Guido Weiss

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© 1982 Springer-Verlag

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Cotlar, M., Sadosky, C. (1982). Majorized toeplitz forms and weighted inequalities with general norms. In: Ricci, F., Weiss, G. (eds) Harmonic Analysis. Lecture Notes in Mathematics, vol 908. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093285

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  • DOI: https://doi.org/10.1007/BFb0093285

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11188-7

  • Online ISBN: 978-3-540-38973-6

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