Certain singular integral operators revisited

Abstract

This note presents an alternate approach to the analysis of the composition of some (classical) singular integral oprators that arise in a number of applications. It is based on the facts that certain naturally paired operators have the same range and are injective. In the course of this analysis the proofs of some classical identities are unified

Keywords:

• Weyl fractional integrals
• Schwartz space
• Fourier transform
• Hilbert transform

AMS(MOS):

• 26A33
• 44A15
• 45