ABSTRACT
Our first lemma, which can be proved by a simple compactness argument, may be viewed as a simple exercise.
Lemma 3.1 Let ∆n := {δ0 < δ1 < · · · < δn} be a set of real numbers. Let a, b, c ∈ R , a < b. Let w = 0 be a continuous function defined on [a, b] . Let q ∈ (0,∞]. Then there exists a 0 = T ∈ E(∆n) such that |T (c)|
‖Tw‖Lq [a,b] = sup
|P (c)| ‖Pw‖Lq [a,b]
,
and there exists a 0 = S ∈ E(∆n) such that |S′(c)|
‖Sw‖Lq [a,b] = sup
.
