Maximal Functions over Hypersurfaces with Flat Points

✍ Scribed by Kyung Soo Rim

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 108 KB
• Volume: 260
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2001.7436

✦ Synopsis

For n G 4, let S be a flat hypersurface in ‫ޒ‬ n , and let d s d , where ϱ Ž n . g C ‫ޒ‬ and is the surface area measure on S. Then the maximal functions 0 Ž . < Ž . Ž . < Ž n . Mf associated to S and by Mf x s sup H f x y t d , f g S S ‫ޒ‬ , are t ) 0 S ⌽ Ž n . bounded on certain Orlicz spaces L ‫ޒ‬ .