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2000 | 138 | 2 | 135-163
Tytuł artykułu

Schauder decompositions and multiplier theorems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the interplay between unconditional decompositions and the R-boundedness of collections of operators. In particular, we get several multiplier results of Marcinkiewicz type for $L^p$-spaces of functions with values in a Banach space X. Furthermore, we show connections between the above-mentioned properties and geometric properties of the Banach space X.
Słowa kluczowe
Czasopismo
Rocznik
Tom
138
Numer
2
Strony
135-163
Opis fizyczny
Daty
wydano
1999-11-22
otrzymano
1998-10-27
Twórcy
autor
  • Department of Mathematics, Faculty ITS, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands., Clement@twi.tudelft.nl
autor
  • Department of Mathematics, Faculty ITS, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands, B.dePagter@twi.tudelft.nl
  • Department of Mathematics and Statistics, The Flinders University of South Australia, G.P.O. Box 2100 Adelaide, South Australia 5001, Australia, sukochev@ist.flinders.edu.au
autor
  • Department of Mathematics, Faculty ITS, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands, H.Witvliet@twi.tudelft.nl
Bibliografia
  • [BG94] E. Berkson and T. A. Gillespie, Spectral decompositions and harmonic analysis on UMD spaces, Studia Math. 112 (1994), 13-49.
  • [Bou83] J. Bourgain, Some remarks on Banach spaces in which martingale differences are unconditional, Ark. Mat. 21 (1983), 163-168.
  • [Bou85] J. Bourgain, Vector-valued singular integrals and the $H^1$-BMO duality, in: Probability Theory and Harmonic Analysis, Dekker, New York, 1985, 1-19.
  • [Bur83] D. Burkholder, A geometric condition that implies the existence of certain singular integrals of Banach-space-valued functions, in: Proc. Conf. on Harmonic Analysis in Honor of Antoni Zygmund (Chicago, 1981), Wadsworth, Belmont, 1983, 270-286.
  • [DJT95] J. Diestel, H. Jarchow and A. Tonge, Absolutely Summing Operators, Cambridge Univ. Press, 1995.
  • [DU77] J. Diestel and J. J. Uhl, Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, RI, 1977.
  • [DS97] P. Dodds and F. Sukochev, Non-commutative bounded Vilenkin systems, preprint, 1997.
  • [EG77] R. E. Edwards and G. I. Gaudry, Littlewood-Paley and Multiplier Theory, Ergeb. Math. Grenzgeb. 90, Springer, Berlin, 1977.
  • [GK70] I. C. Gohberg and M. G. Kreĭn, Theory and Applications of Volterra Operators in Hilbert Space, Transl. Math. Monogr. 24, Amer. Math. Soc., Providence, RI, 1970.
  • [KP79] N. J. Kalton and N. T. Peck, Twisted sums of sequence spaces and the three space problem, Trans. Amer. Math. Soc. 255 (1979), 1-30.
  • [KP70] S. Kwapień and A. Pełczyński, The main triangle projection in matrix spaces and its applications, Studia Math. 34 (1970), 43-68.
  • [LT77] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. I, Ergeb. Math. Grenzgeb. 92, Springer, Berlin, 1977.
  • [Mar39] J. Marcinkiewicz, Sur les multiplicateurs des séries de Fourier, Studia Math. 8 (1939), 78-91.
  • [Mau75] B. Maurey, Système de Haar, in: Séminaire Maurey-Schwartz 1974-1975: Espaces $L_p$, applications radonifiantes et géométrie des espaces de Banach, Exp. Nos. I et II, Centre Math., École Polytech., Paris, 1975, p. 26.
  • [Pal32] R. E. A. C. Paley, A remarkable series of orthogonal functions, Proc. London Math. Soc. 34 (1932), 241-279.
  • [Pis78] G. Pisier, Some results on Banach spaces without local unconditional structure, Composito Math. 37 (1978), 3-19.
  • [SWS90] F. Schipp, W. R. Wade and P. Simon, Walsh Series, Adam Hilger, Bristol, 1990.
  • [Ste70] E. M. Stein, Topics in Harmonic Analysis Related to the Littlewood-Paley Theory, Ann. of Math. Stud. 63, Princeton Univ. Press, Princeton, NJ, 1970.
  • [SF94] A. Sukochev and S. V. Ferleger, Harmonic analysis in symmetric spaces of measurable operators, Dokl. Akad. Nauk 339 (1994), 307-310 (in Russian); English transl.: Russian. Acad. Sci. Dokl. Math. 50 (1995), 432-437.
  • [SF95] F. A. Sukochev and S. V. Ferleger, Harmonic analysis in (UMD)-spaces: Applications to the theory of bases, Mat. Zametki 58 (1995), 890-905 (in Russian); English transl.: Math. Notes 58 (1995), 1315-1326.
  • [Sun51] G. I. Sunouchi, On the Walsh-Kaczmarz series, Proc. Amer. Math. Soc. 2 (1951), 5-11.
  • [Wat58] C. Watari, On generalized Walsh Fourier series, Tôhoku Math. J. (2) 10 (1958), 211-241.
  • [Wen93] J. Wenzel, Mean convergence of vector-valued Walsh series, Math. Nachr. 162 (1993), 117-124.
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Bibliografia
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