Abstract In this paper we study weighted integrability of the sum of double cosine series. The results obtained extend a theorem of 5 onLp-integrability of double cosine series and two theorems of 1 on weightedLp-norms.

Abstract We introduce a new class of double sequences D G M ( α , β , γ , r ) called Double General Monotone and some new class of weight functions to study the weighted integrability of double sine… Expand

The L-convergence of Fourier series problems through additional assumptions for Fourier coefficients were presented by W. H. Young in 1913. We say that they are the classical results. Using modified… Expand

We introduce a new kind of double sequences named MVBVDS and some new classes of weight functions to study the weighted integrability of the double trigonometric series. Several results of Chen,… Expand

We extend from one-dimensional to two-dimensional series the results by Hardy and Littlewood [6] on the Lr-integrability of the sum f and the results by Stechkin [10] on the L'-integrability of the… Expand

(x) is not in general Lebesgue integrable in (0, n) [2, p. 7881. He also proved that for 0 < y < 1 a function like xP’ near 0 has a cosine series whose coefficients behave at infinity like n7-l and… Expand

We prove that if a weakly even sequence {ck: k = 0, ±1, ...} of complex numbers is such that for some p > 1 we have £2"" £ Wck + c_k)f] <oo, I + I = i, then the symmetric partial sums of the… Expand