Abstract: The main aim of this paper is to prove that the maximal operator of a subsequence of the (one-dimensional) logarithmic means of Vilenkin-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 Vilenkin-Fourier series is of weak type (1,1), provided that the supremum in the maximal operator is tak...

lorentz characterized the almost convergence through the concept of uniform convergence of de lavallée-poussin mean. in this paper, we generalize the notion of almost convergence by using the concept ofinvariant mean and the generalized de la vallée-poussin mean. we determine the bounded linear operators forthe generalized σ-conservative, σ-regular and σ-coercive matrices.

the aim of this paper is to introduce and study a new concept of strong double δ ( a ) σ -convergence sequences with respect to an orlicz function, and some properties of the resulting sequencespaces were also examined. in addition, we define the δ ( a ) σ -statistical convergence and establish someconnections between the spaces of strong double δ ( a ) σ -convergence sequences and the space of...

We study pointwise convergence of the solution to elastic wave equation initial data which lies in Sobolev spaces. prove that converges along every line almost everywhere whenever regularity is greater than one half. show this optimal.