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1994-1995 | 112 | 1 | 13-49
Tytuł artykułu

Spectral decompositions and harmonic analysis on UMD spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We develop a spectral-theoretic harmonic analysis for an arbitrary UMD space X. Our approach utilizes the spectral decomposability of X and the multiplier theory for $L_X^p$ to provide on the space X itself analogues of the classical themes embodied in the Littlewood-Paley Theorem, the Strong Marcinkiewicz Multiplier Theorem, and the M. Riesz Property. In particular, it is shown by spectral integration that classical Marcinkiewicz multipliers have associated transforms acting on X.
Słowa kluczowe
Czasopismo
Rocznik
Tom
112
Numer
1
Strony
13-49
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-05-31
Twórcy
autor
  • Department of Mathematics, University of Illinois, 1409 West Green St., Urbana, Illinois 61801, U.S.A.
  • Department of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Edinburgh EH9 3JZ, Scotland
Bibliografia
  • [1] N. Asmar, E. Berkson and T. A. Gillespie, Transferred bounds for square functions, Houston J. Math. 17 (1991), 525-550.
  • [2] N. Asmar, E. Berkson and T. A. Gillespie, Spectral integration of Marcinkiewicz multipliers, Canad. J. Math. 45 (1993), 470-482.
  • [3] E. Berkson, J. Bourgain and T. A. Gillespie, On the almost everywhere convergence of ergodic averages for power-bounded operators on $L^p$-subspaces, Integral Equations Operator Theory 14 (1991), 678-715.
  • [4] E. Berkson and T. A. Gillespie, Fourier series criteria for operator decomposability, ibid. 9 (1986), 767-789.
  • [5] E. Berkson and T. A. Gillespie, Stechkin's theorem, transference, and spectral decompositions, J. Funct. Anal. 70 (1987), 140-170.
  • [6] E. Berkson and T. A. Gillespie, Spectral decompositions and vector-valued transference, in: Analysis at Urbana II (Proceedings of Special Year in Modern Analysis at the Univ. of Ill., 1986-87), London Math. Soc. Lecture Note Ser. 138, Cambridge Univ. Press, Cambridge, 1989, 22-51.
  • [7] E. Berkson and T. A. Gillespie, Transference and extension of Fourier multipliers for $L^p(𝕋)$, J. London Math. Soc. (2) 41 (1990), 472-488.
  • [8] E. Berkson, T. A. Gillespie and P. S. Muhly, Abstract spectral decompositions guaranteed by the Hilbert transform, Proc. London Math. Soc. (3) 53 (1986), 489-517.
  • [9] E. Berkson, T. A. Gillespie and P. S. Muhly, Generalized analyticity in UMD spaces, Ark. Mat. 27 (1989), 1-14.
  • [10] J. Bourgain, Some remarks on Banach spaces in which martingale difference sequences are unconditional, ibid. 21 (1983), 163-168.
  • [11] J. Bourgain, Vector-valued singular integrals and the $H^1$-BMO duality, in: Probability Theory and Harmonic Analysis (Mini-Conference on Probability and Harmonic Analysis, Cleveland, 1983), J.-A. Chao and W. A. Woyczyński (eds.), Monographs and Textbooks in Pure and Appl. Math. 98, Marcel Dekker, New York, 1986, 1-19.
  • [12] D. L. 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), W. Beckner et al. (eds.), Wadsworth, Belmont, Calif., 1983, 270-286.
  • [13] H. R. Dowson, Spectral Theory of Linear Operators, London Math. Soc. Monographs 12, Academic Press, New York, 1978.
  • [14] R. E. Edwards and G. I. Gaudry, Littlewood-Paley and Multiplier Theory, Ergeb. Math. Grenzgeb. 90, Springer, Berlin, 1977.
  • [15] T. A. Gillespie, Commuting well-bounded operators on Hilbert spaces, Proc. Edinburgh Math. Soc. (2) 20 (1976), 167-172.
  • [16] J.-P. Kahane, Sur les sommes vectorielles $∑ ± u_n$, C. R. Acad. Sci. Paris 259 (1964), 2577-2580.
  • [17] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I (Sequence Spaces), Ergeb. Math. Grenzgeb. 92, Springer, Berlin, 1977.
  • [18] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II (Function Spaces), Ergeb. Math. Grenzgeb. 97, Springer, Berlin, 1979.
  • [19] M. Marcus and G. Pisier, Random Fourier Series with Applications to Harmonic Analysis, Ann. of Math. Stud. 101, Princeton University Press, 1981.
  • [20] D. J. Ralph, Semigroups of well-bounded operators and multipliers, Thesis, Univ. of Edinburgh, 1977.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv112i1p13bwm
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