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.
- Abstract Besov space
- Limiting interpolation inequality
- Lorentz spaces
- The K-method
- Uniqueness problems for semilinear evolution equations
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