We prove two-weight norm inequalities for Cesàro means of generalized Hermite polynomial series and for the supremum of these means. A result about weak boundedness and an almost everywhere convergence result are also obtained.

The main aim of this paper is to prove that the maximal operator of a subsequence of the (one-dimensional) logarithmic means of Walsh-Kaczmarz-Fourier series is of weak type (1,1) . Moreover, we prove that the maximal operator of the logarithmic means of quadratical partial sums of double Walsh-Kaczmarz-Fourier series is of weak type (1,1) , provided that the supremum in the maximal operator is...