Weighted generalized functions and hyperbolic Riesz B‐potential. (5th March 2019)

• Record Type: Journal Article
• Authors: Shishkina, Elina
• Other Names: Kravchenko Vladislav V. guestEditor.; Porter R. Michael guestEditor.; Torba Sergii M. guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 15(2019)
• Page Start: 5060
• Page End: 5071
• Publication Date: 2019-03-05
• Subjects: fractional power of singular hyperbolic operator -- generalized translation -- hyperbolic Riesz B‐potential -- Lorentz distance -- multidimensional Hankel transform -- singular Bessel differential operator; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5437
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The paper is devoted to the study of the fractional integral operator, which is a negative real power of the singular wave operator generated by Bessel operator using weighted generalized functions. We give conditions for this operator to be bounded in appropriate spaces, obtain formula for the Hankel transform of this operator, and get formula of connection between this operator and natural degree of singular wave operator generated by Bessel operator.