The Hadamard Fractional Power in Mikhlin-besov Inclusions
نویسندگان
چکیده
Banach algebras defined by fractional Mikhlin-type conditions are continuously contained in Besov spaces, in such a way that the difference between the corresponding degrees of derivation can be made arbitrarily small. In this note a proof of this inclusion is given which is based on the Hadamard fractional operator and its adjoint integration operator on the positive half-line. §
منابع مشابه
General Hörmander and Mikhlin Conditions for Multipliers of Besov Spaces
Abstract. Here a new condition for the geometry of Banach spaces is introduced and the operator–valued Fourier multiplier theorems in weighted Besov spaces are obtained. Particularly, connections between the geometry of Banach spaces and Hörmander-Mikhlin conditions are established. As an application of main results the regularity properties of degenerate elliptic differential operator equation...
متن کاملOn Hadamard and Fej'{e}r-Hadamard inequalities for Caputo $small{k}$-fractional derivatives
In this paper we will prove certain Hadamard and Fejer-Hadamard inequalities for the functions whose nth derivatives are convex by using Caputo k-fractional derivatives. These results have some relationship with inequalities for Caputo fractional derivatives.
متن کاملA generalized form of the Hermite-Hadamard-Fejer type inequalities involving fractional integral for co-ordinated convex functions
Recently, a general class of the Hermit--Hadamard-Fejer inequality on convex functions is studied in [H. Budak, March 2019, 74:29, textit{Results in Mathematics}]. In this paper, we establish a generalization of Hermit--Hadamard--Fejer inequality for fractional integral based on co-ordinated convex functions.Our results generalize and improve several inequalities obtained in earlier studies.
متن کاملAn Existence Theorem for Fractional Hybrid Differential Inclusions of Hadamard Type
This paper studies the existence of solutions for fractional hybrid differential inclusions of Hadamard type by using a fixed point theorem due to Dhage. The main result is illustrated with the aid of an example.
متن کاملFractional Hermite-Hadamard type inequalities for n-times log-convex functions
In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.
متن کامل