| Abstract: | For a real interval I of positive length, we prove a necessary and sufficient condition which ensures that the continuous L p (0 < p ⩽ ∞) norm of a weighted polynomial, P n w n , deg P n ⩽ n, n ⩾ 1 is in an nth root sense, controlled by its corresponding discrete H?lder norm on a very general class of discrete subsets of I. As a by product of our main result, we establish inequalities and theorems dealing with zero distribution, zero location and sup and L p infinite–finite range inequalities. |
