On integrability and L1-convergence differentiated trigonometric series

✍ Scribed by N. Tanović-Miller

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 184 KB
• Volume: 284
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1016/s0022-247x(03)00362-7

✦ Synopsis

New integrability and L 1 -convergence classes for the r-times differentiated trigonometric series k∈Z (ik) r c k e ikx are derived using known results on integrability and L 1 -convergence of trigonometric series. These classes, Theorems 1 and 2, subsume all known integrability and L 1 -convergence classes for differentiated series. In particular, the extensions of the Fomin type theorems to r-times differentiated series, due to S.