1. The convolution algebra H1(R)
- Author
-
R. L. Johnson and C. R. Warner
- Subjects
Mathematics ,QA1-939 - Abstract
H1(R) is a Banach algebra which has better mapping properties under singular integrals than L1(R) . We show that its approximate identity sequences are unbounded by constructing one unbounded approximate identity sequence {vn}. We introduce a Banach algebra Q that properly lies between H1 and L1, and use it to show that c(1 + ln n) ≤ ||vn||H1 ≤ Cn1/2. We identify the maximal ideal space of H1 and give the appropriate version of Wiener's Tauberian theorem.
- Published
- 2010
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