Coincidence criteria for the kernel of a function and the kernel of its integral almost positive means

Abstract

We establish necessary and sufficient conditions for a point A of the Knopp kernelK(f) of a functionf to belong to the kernelK(M) of a functionM(t):=∫ _S fdμ _t , where the so-called almost positive measures μ _t determine a regular method of summation. In particular, this gives coincidence criteria for the kernelsK(f) andK(M)