Mellin transform analysis and integration by parts for Hadamard-type fractional integrals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:270

Article

Butzer, PL ; Kilbas, AA ; Trujillo, JJ

关键词: Hadamard-type fractional integration;    spaces of p-summable functions;    Mellin transforms;    fractional integration by parts;   

DOI  :  10.1016/S0022-247X(02)00066-5

来源: Elsevier

【 摘 要 】

This paper is devoted to the study of four integral operators that are basic generalizations and modifications of fractional integrals of Hadamard, in the space X-C(P) of Lebesgue measurable functions f on R+ = (0, infinity) such that integral(0)(infinity)\u(c)f(u)\(p)du/u < infinity (1 less than or equal to p less than or equal to infinity), ess sup(u>0)[u(c)\f(u)\] < infinity (p = infinity), for c is an element of R = (-infinity, infinity), in particular in the space L-p (0, infinity) (1 less than or equal to p less than or equal to infinity). Formulas for the Mellin transforms of the four Hadamard-type fractional integral operators are established as well as relations of fractional integration by parts for them. (C) 2002 Elsevier Science (USA). All rights reserved.

【 授权许可】

Free