Almost Everywhere Convergence of the Cesàro Means of Two Variablewalsh–Fourier Series with Variable Parameters

Ukrainian Mathematical Journal - It is shown that the maximal operator of some (C, βn)-means of cubical partial sums of two variable Walsh–Fourier series of integrable functions is of...     

Convergence of the Cesàro mean for rational orthonormal bases

This paper deals with the convergence of the Cesaro mean for the rational orthonormal bases. Provided the set of zeroes of rational orthonormal bases is formed by a periodic repetition of the same finite sequence, the explicit expression of so-called block-Fejer kernel is available, and some properties of the block-Fejer kernel are discussed. Based on the convergence of the block-Cesaro mean, the convergence of Cesaro mean is also provided.