Abstract
This paper considers the modified fractional integral operators involving the Gauss hypergeometric function and obtains weighted inequalities for these operators. Multidimensional fractional integral operators involving the H-function are also introduced.
Highlights
Introduction and preliminariesTuan and Saigo [7] introduced the multidimensional modified fractional integrals of order α (Re(α) > 0) by X+α;n f (x) = 1 Γ(α + 1) Dn Rn+ min x1 t1, xn tn α − 1 f (t)dt, +
This paper considers the modified fractional integral operators involving the Gauss hypergeometric function and obtains weighted inequalities for these operators
We introduce the following classes of multidimensional modified fractional integral operators involving the well-known H-function [2, Section 8.3] defined by HMP,Q,N,+;n f
Summary
Tuan and Saigo [7] introduced the multidimensional modified fractional integrals of order α (Re(α) > 0) by. The operators in (1.1) provide multidimensional generalizations to the well-known one-dimensional Riemann-Liouville and Weyl fractional integral operators defined in [5] (see [1]). By invoking the Gauss hypergeometric function 2F1(α, β; γ; x), the following generalizations of the multidimensional modified integral operators (1.1) of order α (Re(α) > 0). For β = −α, the operators (1.3) and (1.4) reduce to the modified integral operators defined in (1.1), respectively. In [8], the integral operators X+α;n f (x) and X−α;n f (x) defined on the space ᏹγ(Rn+) are shown to satisfy some Lp − Lq weighted inequalities. The present paper is devoted to finding inequalities for the generalized multidimensional modified integral operators (1.3) and (1.4) by making use of the inequality stated in [8] (which was established with the aid of Pitt’s inequality). The operator xhSα+,;βn,γx−h f (x) is a homeomorphism of the space ᏹ1/2(Rn+) onto itself, and xhSα+,;βn,γx−h f (x)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Mathematics and Mathematical Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
