A Characterization of the Interpolation Spaces of H ~ and L ~ 176 on the Line
نویسنده
چکیده
Let Xo and X, be two Banach spaces which are continuously embedded in a common Hausdort t topological vector space. An admissible operator for the pair (Xo, X,) is a linear operator whose domain contains the union of the two spaces and whose restrictions to Xi is a bounded operator on Xi ( i = 0 , 1). A space X is called an interpolation space for the pair (Xo, X,) if each admissible operator T is bounded on X. For a measurable function ~ let r denote its nonincreasing rearrangement (see [4] or [2] for details). In [4] Calder6n showed that the interpolation spaces o f L ~ and L ~ are characterized in terms of a quasi-order < (the Hardy-Li t t lewoodP61ya relation) involving the rearrangements r
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