For real functions of bounded variation in the Hardy sense, -periodic in each variable, the rates of pointwise convergence of the Borel and Euler means of their Fourier series are estimated.
MSC 2010: 42A32; 42A20In this paper we have defined a new class of double numerical sequences. If the coefficients of a double cosine or sine trigonometric series belong to the such classes, then it is verified that they are Fourier series or equivalently their sums are integrable functions. In addition, we obtain an estimate for the mixed modulus of smoothness of a double sine Fourier series whose coefficients belong to the new class of sequences mention above.
The concepts of statistical convergence of single and double sequences of complex numbers were introduced in [1] and [7], respectively. In this paper, we introduce the concept indicated in the title. A double sequence is said to be regularly statistically convergent if (i) the double sequence is statistically convergent to some ξ ∈ ℂ, (ii) the single sequence is statistically convergent to some for each fixed j ∈ ℕ ∖ ₁, (iii) the single sequence is statistically convergent to some for...
Several new integrability theorems are proved for multiple cosine or sine series.