On the monotonicity of some singular integral operators

The paper deals with the monotonicity of singular integral operators of the form Q = q S where S is the Cauchy singular integral operator on the interval (0,1) of the real axis R and q is a power or logarithmic function. Under suitable assumptions, such singular integral operators are proved to be monotone and maximal monotone inL 2spaces with power weights. Moreover, two related integral equations with weakly singular kernels of logarithmic type are studied. Copyright © 2012 John Wiley & Sons, Ltd.