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1993 | 104 | 2 | 133-150
Tytuł artykułu

Interpolation of operators when the extreme spaces are $L^{∞}$

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Języki publikacji
EN
Abstrakty
EN
Under some assumptions on the pair $(A_0,B_0)$, we study equivalence between interpolation properties of linear operators and monotonicity conditions for a pair (Y,Z) of rearrangement invariant quasi-Banach spaces when the extreme spaces of the interpolation are $L^∞$. Weak and restricted weak intermediate spaces fall within our context. Applications to classical Lorentz and Lorentz-Orlicz spaces are given.
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Twórcy
  • Departamento de Matemáticas, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain.
  • Departamento de Matemáticas, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain.
Bibliografia
  • [1] M. A. Ariño and B. Muckenhoupt, Maximal functions on classical Lorentz spaces and Hardy's inequality with weights for nonincreasing functions, Trans. Amer. Math. Soc. 320 (2) (1990), 727-735.
  • [2] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, 1988.
  • [3] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, 1976.
  • [4] D. W. Boyd, Indices of function spaces and their relationship to interpolation, Canad. J. Math. 21 (1969), 1245-1254.
  • [5] A. P. Calderón, Spaces between $L^1$ and $L^∞$ and the theorem of Marcinkiewicz, Studia Math. 26 (1966), 273-299.
  • [6] M. Cwikel, K-divisibility of the K-functional and Calderón couples, Ark. Mat. 22 (1) (1984), 39-62.
  • [7] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math. Stud. 116, North-Holland, Amsterdam 1985.
  • [8] N. J. Kalton, Endomorphisms of symmetric function spaces, Indiana Univ. Math. J. 34 (2) (1985), 225-247.
  • [9] A. Kamińska, Some remarks on Orlicz-Lorentz spaces, Math. Nachr. 147 (1990), 29-38.
  • [10] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Springer, 1979.
  • [11] G. Lorentz and T. Shimogaki, Interpolation theorems for the pairs of spaces $(L^p, L^∞)$ and $(L^1, L^q)$, Trans. Amer. Math. Soc. 139 (1971), 207-221.
  • [12] L. Maligranda, A generalization of the Shimogaki theorem, Studia Math. 71 (1981), 69-83.
  • [13] L. Maligranda, Indices and interpolation, Dissertationes Math. 234 (1985).
  • [14] M. Mastyło, Interpolation of linear operators in Calderón-Lozanovskii spaces, Comment. Math. 26 (2) (1986), 247-256.
  • [15] S. J. Montgomery-Smith, Comparison of Orlicz-Lorentz spaces, Studia Math. 103 (1992), 161-189.
  • [16] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226.
  • [17] Y. Raynaud, On Lorentz-Sharpley spaces, in: Proc. Workshop "Interpolation Spaces and Related Topics", Haifa, June 1990, IMCP, Vol. 5 (1992), 207-228.
  • [18] E. Sawyer, Boundedness of classical operators on classical Lorentz spaces, Studia Math. 96 (1990), 145-158.
  • [19] R. Sharpley, Spaces $Λ_α (X)$ and interpolation, J. Funct. Anal. 11 (1972), 479-513.
  • [20] T. Shimogaki, An interpolation theorem on Banach function spaces, Studia Math. 31 (1968), 233-240.
  • [21] A. Torchinsky, Interpolation of operators and Orlicz classes, ibid. 59 (1976), 177-207.
  • [22] M. Zippin, Interpolation of operators of weak type between rearrangement invariant function spaces, J. Funct. Anal. 7 (1971), 267-284.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv104i2p133bwm
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