Compactness of a class of Volterra operators
S. D. Riemenschneider · Tohoku Mathematical Journal · 1974
A necessary and sufficient condition is given for integral operators of the formRecently, D. W. Boyd and J. A. Erdδs [1] established necessary and sufficient conditions for certain integral operators to map L p [0, 1] into itself.It turns out that this result was proven earlier in the form of a generalized Hardy's inequality (see Muckenhoupt [4] for a simple proof and earlier references).Using their methods and a theorem of Ando, we give necessary and sufficient conditions for the operators to be compact.The integral operators are of the form Tf(x) = h(x)[k(t)f(t)dtJo * Supported in part by Canadian NRC grant A-7687.