Compacts de fonctions de première classe
Mathematics Subject Classification: 74D05, 26A33In this paper, a comparative analysis of the models involving fractional derivatives of di®erent orders is given. Such models of viscoelastic materials are widely used in various problems of mechanics and rheology. Rabotnov's hereditarily elastic rheological model is considered in detail. It is shown that this model is equivalent to the rheological model involving fractional derivatives in the stress and strain with the orders proportional to a certain positive...
A unified approach to prove isoperimetric inequalities for moments and basic inequalities of interpolation spaces L(p,q) is developed. Instead symmetrization methods we use a monotonicity property of special Stiltjes' means.
Let with , and , and let where We establish the asymptotic expansion where stands for the Bernoulli polynomials. Further, we prove that the functions and are completely monotonic in on for every if and only if and , respectively. This not only unifies the two known results but also yields some new results.
2000 Mathematics Subject Classification: 30C10.Classical Rolle’s theorem and its analogues for complex algebraic polynomials are discussed. A complex Rolle’s theorem is conjectured.
We present the complex interpolation of Besov and Triebel–Lizorkin spaces with generalized smoothness. In some particular cases these function spaces are just weighted Besov and Triebel–Lizorkin spaces. As a corollary of our results, we obtain the complex interpolation between the weighted Triebel–Lizorkin spaces and with suitable assumptions on the parameters and , and the pair of weights .