ALMOST EVERYWHERE CONVERGENCE OF CONE-LIKE RESTRICTED TWO-DIMENSIONAL FEJER MEANS WITH RESPECT TO VILENKIN-LIKE SYSTEMS

For the two-dimensional Walsh system, Gat and Weisz proved the a. e. convergence of the Fejer means sigma(n)f of integrable functions, where the set of indices is inside a positive cone around the identical function, that is, beta(-1) <= n(1)/n(2) <= beta, with some fixed parameter beta >= 1. The result of Gat and Weisz was generalized by G ' at and the author in the way that the indices are inside a cone-like set. In the present paper, the a. e. convergence is proved for the Fejer means of integrable functions with respect to two-dimensional Vilenkin-like systems provided that the set of indeces is in a cone-like set. That is, the result of Gat and the author is generalized to a general orthonormal system, which contains as special cases the Walsh system, the Vilenkin system, the character system of the group of 2-adic integers, the UDMD system, and the representative product system of CTD (compact totally disconnected) groups.