AbstractThe first part of this paper complements previous results on characterization of polynomials of least deviation from zero in Sobolev p-norm ($$1<p<\infty $$
1
<
p
<
∞
) for the case $$p=1$$
p
=
1
. Some relevant examples are indicated. The second part deals with the location of zeros of polynomials of least deviation in discrete Sobolev p-norm. The asymptotic distribution of zeros is established on general conditions. Under some order restriction in the discrete part, we prove that the n-th polynomial of least deviation has at least $$n-\mathbf {d}^*$$
n
-
d
∗
zeros on the convex hull of the support of the measure, where $$\mathbf {d}^*$$
d
∗
denotes the number of terms in the discrete part.