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2000 | 138 | 3 | 251-264

Tytuł artykułu

Partial retractions for weighted Hardy spaces

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
Let 1 ≤ p ≤ ∞ and let $w_0, w_1$ be two weights on the unit circle such that $log(w_0w_1^{-1})∈ BMO$. We prove that the couple $(H_p(w_0), H_p(w_1))$ of weighted Hardy spaces is a partial retract of $(L_p(w_0), L_p(w_1))$. This completes previous work of the authors. More generally, we have a similar result for finite families of weighted Hardy spaces. We include some applications to interpolation.

Słowa kluczowe

Czasopismo

Rocznik

Tom

138

Numer

3

Strony

251-264

Daty

wydano
2000
otrzymano
1999-03-29

Twórcy

  • Steklov Math. Institute, St. Petersburg Branch, Fontanka 27, 191011 St. Petersburg, Russia.
autor
  • Université de Franche-Comté, UMR de Mathématiques, 16, Route de Gray, 25030 Besançon Cedex, France.

Bibliografia

  • [1] J. Bergh and J. Löfström, Interpolation Spaces, Springer, Berlin, 1976.
  • [2] Yu. A. Brudnyi and N. Ya. Krugljak, Real Interpolation Functors and Interpolation Spaces I, North-Holland, 1991.
  • [3] F. Cobos and J. Peetre, Interpolation of compact operators: the multidimensional case, Proc. London Math. Soc. 63 (1991), 371-400.
  • [4] R. Coifman, M. Cwikel, R. Rochberg, Y. Sagher and G. Weiss, A theory of complex interpolation for families of Banach spaces, Adv. Math. 43 (1982), 203-229.
  • [5] M. Cwikel, J. E. McCarty and T. H. Wolff, Interpolation between weighted Hardy spaces, Proc. Amer. Math. Soc. 116 (1992), 381-388.
  • [6] S. Janson, Interpolation of subcouples and quotient couples, Ark. Mat. 31 (1993), 307-338.
  • [7] N. Kalton, Complex interpolation of Hardy-type subspaces, Math. Nachr. 171 (1995), 227-258.
  • [8] S. V. Kisliakov, Interpolation of $H^p$-spaces: some recent developments, in: Function Spaces, Interpolation Spaces, and Related Topics, Israel Math. Conf. Proc. 13, Bar-Ilan Univ., Ramat Gan, 1999, 102-140.
  • [9] S. V. Kisliakov, Bourgain's analytic projection revisited, Proc. Amer. Math. Soc. 126 (1998), 3307-3314.
  • [10] S. V. Kisliakov and Q. Xu, Interpolation of Hardy spaces, Trans. Amer. Math. Soc. 343 (1994), 1-34.
  • [11] S. V. Kisliakov and Q. Xu, Real interpolation and singular integrals, St. Petersburg Math. J. 8 (1997), 593-615.
  • [12] G .Pisier, Interpolation between $H^p$ spaces and non-commutative generalizations, I, Pacific J. Math. 155 (1992), 341-368.
  • [13] Q. Xu, Notes on interpolation of Hardy spaces, Ann. Inst. Fourier (Grenoble) 42 (1992), 875-889; Erratum, 43 (1993), 569.
  • [14] Q. Xu, New results on interpolation of Hardy spaces, in: Banach Space Theory and its Applications (Wuhan, 1994), Wuhan Univ. Press, 1996, 13-31.

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