It is proved that the maximal operator of the l1-Fejér means of a d-dimensional Fourier series is bounded from the periodic Hardy space Hp(T ) to L p(T ) for all d/(d+1) < p ≤ ∞ and, consequently, is of weak type (1, 1). As a consequence we obtain that the l1-Fejér means of a function f ∈ L1(T ) converge a.e. to f . Moreover, we prove that the l1-Fejér means are uniformly bounded on the spaces ...

Some recent results on a general summability method, on the so-called θ-summability is summarized. New spaces, such as Wiener amalgams, Feichtinger’s algebra and modulation spaces are investigated in summability theory. Sufficient and necessary conditions are given for the norm and a.e. convergence of the θ-means.

The primary objective of this study is to extend the concept strongly I-deferred Ces?ro summability and ?-deferred I-statistical convergence on amenable semigroups. Furthermore, under few conditions, we also establish some inclusion-based results. After that, introduce I*-statistical convergent, I-statistically pre-Cauchy, I*-statistically pre-Cauchy functions in semigroups prove results based ...

In the classical summability setting rates of summation have been introduced in several ways (see, e.g., [10], [21], [22]). The concept of statistical rates of convergence, for nonvanishing two null sequences, is studied in [13]. Unfortunately no single de...nition seems to have become the “standard” for the comparison of rates of summability transforms. The situation becomes even more uncharte...

Let ∆xf(x, y) = f(x + 1, y) − f(x, y) and ∆yf(x, y) = f(x, y + 1) − f(x, y) be the difference operators with respect to x and y. A rational function f(x, y) is called summable if there exist rational functions g(x, y) and h(x, y) such that f(x, y) = ∆xg(x, y)+ ∆yh(x, y). Recently, Chen and Singer presented a method for deciding whether a rational function is summable. To implement their method ...