In 2007 Akhobadze [1] (see also [2]) introduced the notion of Cesàro means of Fourier series with variable parameters. In the present paper we prove the almost everywhere convergence of the the Cesàro .C;˛n/ means of integrable functions ˛n n f ! f , where N˛; K 3 n ! 1 for f 2 L 1 .I /, where I is the Walsh group for every sequence˛D .˛n/, 0 <˛n < 1. This theorem for constant sequences˛that is,˛Á˛1 was proved by Fine [3].
UDC 517.5
We prove that the maximal operator of some means of cubical partial sums of two variable Walsh – Fourier series of integrable functions is of weak type . Moreover, the -means of the function converge a.e. to for , where is the Walsh group for some sequences .
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