Abstract
We investigate the real and complex interpolation of L p -spaces and Lorentz spaces over a measure space. In particular, we prove a generalized version of the Marcinkiewicz theorem (the Calderón-Marcinkiewicz theorem). We also investigate the real and the complex interpolation spaces between L p -spaces with different measures, thus extending a theorem by Stein and Weiss. In Section 6, we consider the interpolation of vector-valued L p -spaces of sequences, thus preparing for the interpolation of Besov spaces in the next chapter.
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© 1976 Springer-Verlag Berlin Heidelberg
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Bergh, J., Löfström, J. (1976). Interpolation of L p -Spaces. In: Interpolation Spaces. Grundlehren der mathematischen Wissenschaften, vol 223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-66451-9_5
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DOI: https://doi.org/10.1007/978-3-642-66451-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-66453-3
Online ISBN: 978-3-642-66451-9
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