Abstract
In this chapter we develop a multi-component version of the Riesz-Thorin interpolation theorem and use it to derive a number of Lp inequalities which are natural relatives of inequality (4.15) and the now standard inequalities of Clarkson. These inequalities are crucial to the problem of extending Lipschitz-Hölder maps of order a between Lp spaces (see §19). In addition they are of considerable intrinsic interest, a point we here emphasize by applying certain of their number to a packing problem in Lp.
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© 1975 Springer-Verlag Berlin Heidelberg
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Wells, J.H., Williams, L.R. (1975). Interpolation and Lp Inequalities. In: Embeddings and Extensions in Analysis. Ergebnisse der Mathematik und ihrer Grenzgebiete Band 84, vol 84. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-66037-5_4
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DOI: https://doi.org/10.1007/978-3-642-66037-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-66039-9
Online ISBN: 978-3-642-66037-5
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