Extensions of Móricz Classes and Convergence of Trigonometric Sine Series in <i>L</i>¹-Norm

Abstract

In this paper, the extensions of classes S ˜ ,   C ˜ and B ˜ V are made by defining the classes S ˜ r , C ˜ r and B ˜ V r , r = 0 , 1 , 2 , … It is also shown that class S ˜ r is a subclass of C ˜ r ∩ B ˜ V r . Moreover, the results on L 1 -convergence of r times differentiated trigonometric sine series have been obtained by considering the r t h   ( r = 0 , 1 , 2 , … ) derivative of modified sine sum under the new extended class C ˜ r ∩ B ˜ V r .

Keywords

• Dirichlet kernel
• <i>L</i>¹-convergence
• modified sine sum