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, and
introduce a Banach algebra Q that properly lies between
H1 and L1, and use it to show that the
approximate identity sequence vn satisfies
c (1 + ln n) ≤ ||vn||H1 ≤
Cn½.
We identify the maximal ideal space of H1 and give the
appropriate versions of Wiener's ideal theorem and Wiener's Tauberian
theorem.
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Last modified: April 11 2016 - 18:14:43