Mellin transform analysis and integration by parts for Hadamard-type fractional integrals
نویسندگان
چکیده
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 of Lebesgue measurable functions f on R+ = (0,∞) such that ∞ ∫ 0 ∣∣ucf (u)∣∣p du u <∞ (1 p <∞), ess sup u>0 [ u ∣∣f (u)∣∣]<∞ (p =∞), for c ∈ R = (−∞,∞), in particular in the space Lp(0,∞) (1 p ∞). 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. 2002 Elsevier Science (USA). All rights reserved.
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