The convolution algebra H 1(R)

H 1(r) is a banach algebra which has better mapping properties under singular integrals than l 1(r). we show that its approximate identity sequences are unbounded by constructing one unbounded approximate identity sequence {ν n}. we introduce a banach algebra q that properly lies between h 1 and l 1,and use it to show that c(1 + ln n) ≤ ∥ν n∥h 1 ≤ cn 1/2. we identify the maximal ideal space of h 1 and give the appropriate version of wiener's tauberian theorem. copyright © 2010 hindawi publishing corporation.