Abstract
The generalized Lipschitz space generated via fractional powers of differences of semigroup operators on a Banach space X is defined with respect to rearrangement-invariant norms. The Boyd indices of the norm are used as an instrument to yield a reprensentation of this Lipschitz space as an interpolation space. In this frame theorems of interpolation of Riesz-Thorin-type, of reduction and duality are established. The case of optimal approximation as well as particular norms such as the Lebesgue-, Lorentz-, and Orlicz norm are subsumed.
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Fehér, F. (1978). Fractional Lipschitz Spaces Generated by Rearrangement-Invariant Norms. In: Butzer, P.L., Szökefalvi-Nagy, B. (eds) Linear Spaces and Approximation / Lineare Räume und Approximation. International Series of Numerical Mathematics / Intermationale Schriftenreihe zur Numberischen Mathematik / Sùrie Internationale D’analyse Numùruque, vol 40. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7180-8_15
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DOI: https://doi.org/10.1007/978-3-0348-7180-8_15
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