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 ...

Wedetermine the degree of approximation of conjugate of a function belonging to Lip(ξ(t),p) class by matrix summability means of a conjugate series of a Fourier series. 2000 Mathematics Subject Classification. 42B05, 42B08.

In this paper we deal with a main theorem on the local property of ∣∣N, pn∣∣k, k ≥ 1 summability of factored Fourier series, which generalizes some known results. Mathematics Subject Classification: 40D15, 40G99, 42A24, 42B15

Quite recently, Bor (2021) [22] has proved two main theorems dealing with absolute Riesz summability factors of infinite series and Fourier by using an almost increasing sequence. In this paper, we have generalized these to the | A , p n k method.

We consider a perturbed system of exponents { en } n∈Z, when the sequence {λn }n∈Z has a definite asymptotics. We study basis properties (completeness, minimality, basicity) of this system in Lebesgue space of functions Lp(·) (−π, π) with variable summability exponent p(·), subject to parameters contained in the asymptotics {λn}n∈Z.

A set of regular summations logarithmic methods is introduced. This set includes Riesz and Nörlund logarithmic methods as limit cases. The application to logarithmic summability of Fourier series of continuous and integrable functions are given. The kernels of these logarithmic methods for trigonometric system are estimated.

In this article we introduce the notion of different types of statistically convergent and statistically null fuzzy real-valued double sequence spaces. We study their different properties like solidness, symmetric, convergence free, sequence algebra etc. The fuzzy real-valued Cesàro summable double sequence space is introduced. A relation between strongly p-Cesàro summability and bounded statis...