Integrability Properties of the Maximal Operator on Partial Sums of Fourier Series in Orlicz Spaces

✍ Scribed by Hiro-O Kitax

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 540 KB
• Volume: 193
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19981930107

✦ Synopsis

Abstract

Let S* (f be the majorant function of the partial sums of the trigonometric Fourier series of f. In this paper we consider the Orlicz space __L__π and give a generalization of Soria's result [S1]. Let π (t) be a concave function with some nice properties and
. If there exists a positive constant a~0~ < 1 such that
then we have
.