Maximal Averages over Surfaces

✍ Scribed by A Iosevich; E Sawyer

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 682 KB
• Volume: 132
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.1997.1678

✦ Synopsis

denote the maximal operator associated with surface measure d_ on a smooth surface S. We prove that if S is convex and has finite order contact with its tangent lines, then M is bounded on L p (R n ), p>2, if and only if d(x, H) &1 # L 1Âp loc (S) for all tangent planes H not passing through the origin. Let