We consider the group T a , its group of characters Z a , and an arbitrary order P on Z a . For x ∊ Z a , let sgnp x be 1, - 1 , or 0 according as x € P\{0}, x € (-P)\{0}, or X = 0. For f in Lp (T a ), 1 < p < ∞, it is known that there is a function
in Lp (T a ) such that
for all X in Z a . Summability methods for
are also available. In this paper, we obtain summability methods for
that apply for
in L1 (T a ), and we show how various properties of
can be derived from our construction.