Regularization of a generalized abel integral equation

Abstract

The integral equation

where 0<α<1, is considered under appropriate assumptions on K: For the approximate equation Au ≍ g regularization schemes are developed: (i) in L_p,(ii) in the space of functions of bounded variation, (iii) in the space of functions that are Hölder continuous of order γ where 0 <γ<1. The extra information is in case in case ,in case (i), in case (ii)Var , in case (iii) .

Keywords:

• Abel integral equation

AMS:

• 45D05