Let
G be a locally compact group and let
p
(1,∞). Let
A be any of the Banach spaces
Cδ,p(G),
PFp(G),
Mp(G),
APp(G),
WAPp(G),
UCp(G),
PMp(G), of convolution operators on
Lp(G). It is shown that
PFp(G)′ can be isometrically embedded into
UCp(G)′. The structure of maximal regular ideals of
A′ (and of
MAp(G)″,
Bp(G)″,
Wp(G)″) is studied. Among other things it is shown that every maximal regular left (right, two sided) ideal in
A′ is either
weak* dense or is the annihilator of a unique element in the spectrum of
Ap(G). Minimal ideals of
A′ is also studied. It is shown that a left ideal
M in
A′ is minimal if and only if
M=CΨ, where
Ψ is either a right annihilator of
A′ or is a topologically
x-invariant element (for some
x
G). Some results on minimal right ideals are also given.