Norm and almost everywhere convergence of matrix transform means of Walsh-Fourier series
Norm and almost everywhere convergence of matrix transform means of Walsh-Fourier series
Abstract We show the uniformly boundedness of the L 1 norm of general matrix transform kernel functions with respect to the Walsh-Paley system. Special such matrix means are the well-known Cesàro, Riesz, Bohner-Riesz means. Under some conditions, we verify that the kernels <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mrow> <m:msubsup> <m:mrow> <m:mtext>K</m:mtext> </m:mrow> …