Anisotropic Franklin bases on polygonal domains

✍ Scribed by George Kyriazis; Kyungwon Park; Pencho Petrushev

• Book ID: 102490168
• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 352 KB
• Volume: 279
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200510412

✦ Synopsis

Abstract

Franklin systems induced by Courant elements over multilevel nested triangulations of polygonal domains in ℝ^2^ are explored. Mild conditions are imposed on the triangulations which prevent them from deterioration and at the same time allow for a lot of flexibility and, in particular, arbitrarily sharp angles. It is shown that such anisotropic Franklin systems are Schauder bases for C and L ~1~, and unconditional bases for L~p~ (1 < p < ∞) and the corresponding Hardy spaces H ~1~. It is also proved that the anisotropic H ~1~ is exactly the space of all functions in L ~1~ for which the corresponding Franklin system expansions converge unconditionally in L ~1~. Finally, it is shown that the Franklin bases characterize the corresponding anisotropic BMO spaces. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)