A characterization of structural nikolskiî- besov spaces using fractional derivatives Report as inadecuate




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The Nikolskiî-Besov spaces BapqRn, 1 0, are defined in terms of modulus of continuity and they are characterized using the partial derivatives of the Poisson integrals. In this work we show a characterizationof the functions of BapqRn using the Caputo noninteger orderderivative of the Poisson integral.

Tipo de documento: Artículo - Article

Palabras clave: fractional derivatives, Poisson Kernel, Pisson integral





Source: http://www.bdigital.unal.edu.co


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Bol.
Mat.
17(1), 77–98 (2010) 77 A characterization of structural Nikol’skiı̆–Besov spaces using fractional derivatives1 Francisco Enrı́quez2 Alex Montes3 Jhon Pérez4 Departamento de Matemáticas Universidad del Cauca Colombia α (Rn ), 1 ≤ p, q ≤ ∞, α 0, are defined The Nikol’skiı̆–Besov spaces Bpq in terms of modulus of continuity and they are characterized using the partial derivatives of the Poisson integrals.
In this work we show a characα terization of the functions of Bpq (Rn ) using the Caputo noninteger order derivative of the Poisson integral. Keywords: Nikol’skiı̆–Besov spaces, fractional derivative, Poisson kernel, Poisson integral. α Los espacios de Nikol’skiı̆–Besov Bpq (Rn ), 1 ≤ p, q ≤ ∞, α 0, están definidos en términos de módulos de continuidad y se caracterizan usando las derivadas parciales de las integrales de Poisson.
En este trabajo α (Rn ) usando la mostramos una caracterización de las funciones de Bpq derivada de orden no–entero de Caputo de la integral de Poisson. Palabras claves: espacios de Nikol’skiı̆–Besov, derivada fraccional, kernel de Poisson, integral de Poisson. MSC: 26A33, 26A16. 1 This work was supported by the Universidad del Cauca, Popayán, Colombia (2477). 2 enriquezfran@unicauca.edu.co 3 amontes@unicauca.edu.co 4 jjperez@unicauca.edu.co 78 1 Enrı́quez, Montes and Pérez, A characterization Introduction p f (x) The idea of generalizing the notion of differentiation d dx to noninteger p orders of p appeared at the birth of the differential calculus itself.
The first attempt to discuss such an idea recorded in history was contained in the correspondence of Leibniz.
In one of his letters to Leibniz concerning the theorem on the differentiation of a product of functions, Bernoulli asked about the meaning of this theorem in the case of noninteger order of differentiation.
Leibniz in his letters to L’Hôpital (1695) made some remarks on the possi...






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