Kulwinder Kaur, S. S. Bhatia, Babu Ram

Integrability and L¹-Convergence of Modified Sine Sums

Abstract:
New modified sine sums are introduced and a criterion for the $L^{1}$-convergence of these modified sine sums under a new class $\mathit{K}$ is obtained. Also a necessary and sufficient condition for the $L^{1}$-convergence of the cosine series is deduced as a corollary.

Keywords:
$L^{1}$-convergence, modified sine sums, conjugate Fejer kernel.

MSC 2000: 42A20, 42A32.