On fractional convolutions and distributions

Abstract

The present paper focuses on three types of fractional convolutions. First consideration is to extend the famous Young's inequality in the context of fractional convolution. Then for these convolutions, weighted iterated $L^p-L^q$ inequalities have been investigated. Finally, the notion of fractional convolutions between functions and distributions and also between distributions has been defined and various corresponding properties have been studied.

Keywords:

• convolution
• fractional convolution
• weighted convolution inequality
• distribution

2010 AMS Subject Classification:

• 44A35
• 46T30
• 26D20

Disclosure statement

No potential conflict of interest was reported by the authors.