Interpolation inequality of logarithmic type in abstract Besov spaces and an application to semilinear evolution equations |
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| Authors: | Toshitaka Matsumoto Takayoshi Ogawa |
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| Affiliation: | 1. Department of Mathematical and Life Sciences, Hiroshima University, Higashi‐Hiroshima 739‐8526, Japan;2. Mathematical Institute, Tohoku University, Sendai 980‐8578, Japan |
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| Abstract: | An abstract version of Besov spaces is introduced by using the resolvent of nonnegative operators. Interpolation inequalities with respect to abstract Besov spaces and generalized Lorentz spaces are obtained. These inequalities provide a generalization of Sobolev inequalities of logarithmic type. Uniqueness problems to abstract semilinear evolution equations are also discussed (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Abstract Besov space Lorentz spaces the K ‐method limiting interpolation inequality uniqueness problems for semilinear evolution equations |
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