Abstract
We apply Christ’s method of refinements to the ell ^p-improving problem for discrete averages {mathcal {A}}_N along polynomial curves in {mathbb {Z}}^d. Combined with certain elementary estimates for the number of solutions to certain special systems of diophantine equations, we obtain some restricted weak-type p rightarrow p' estimates for the averages {mathcal {A}}_N in the subcritical regime. The dependence on N of the constants here obtained is sharp, except maybe for an epsilon -loss.
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