On a generalization of Lipschitz's classes.
On a Monotonic Trigonometric Sum.
On belonging of trigonometric series to Orlicz space.
On integrability of functions defined by trigonometric series.
On convergence of certain cosine sums.
On convergence of certain cosine sums with twice quasi semi-convex coefficients.
On integrability and convergence of trigonometric series
We first give a necessary and sufficient condition for , 1 < p < ∞, 1/p - 1 < γ < 1/p, where ϕ(x) is the sum of either or , under the condition that λₙ (where λₙ is aₙ or bₙ respectively) belongs to the class of so called Mean Value Bounded Variation Sequences (MVBVS). Then we discuss the relations among the Fourier coefficients λₙ and the sum function ϕ(x) under the condition that λₙ ∈ MVBVS, and deduce a sharp estimate for the weighted modulus of continuity of ϕ(x) in norm.
On some transforms of trigonometric series.
On the behavior of -derivative near the origin of sine series with convex coefficients.
On the integrability and L¹-convergence of double trigonometric series
On the integrability and L¹-convergence of sine series
On the -convergence of Fourier series
Since the trigonometric Fourier series of an integrable function does not necessarily converge to the function in the mean, several additional conditions have been devised to guarantee the convergence. For instance, sufficient conditions can be constructed by using the Fourier coefficients or the integral modulus of the corresponding function. In this paper we give a Hardy-Karamata type Tauberian condition on the Fourier coefficients and prove that it implies the convergence of the Fourier series...
On the uniform convergence of double sine series
Let a single sine series (*) be given with nonnegative coefficients . If is a “mean value bounded variation sequence” (briefly, MVBVS), then a necessary and sufficient condition for the uniform convergence of series (*) is that as k → ∞. The class MVBVS includes all sequences monotonically decreasing to zero. These results are due to S. P. Zhou, P. Zhou and D. S. Yu. In this paper we extend them from single to double sine series (**) , even with complex coefficients . We also give a uniform...
On the uniform convergence of weighted trigonometric series
In the present paper we consider a new class of sequences called GM(β,r), which is the generalization of a class defined by Tikhonov in [15]. We obtain sufficient and necessary conditions for uniform convergence of weighted trigonometric series with (β,r)-general monotone coefficients.
On the utility of the Telyakovskiĭ's class .