@article { , title = {Some Subcritical Estimates for the ℓp-Improving Problem for Discrete Curves}, abstract = {We apply Christ’s method of refinements to the ℓ\^p-improving problem for discrete averages AN along polynomial curves in 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→p′ estimates for the averages A\_N in the subcritical regime. The dependence on N of the constants here obtained is sharp, except maybe for an ϵ-loss.}, doi = {10.1007/s00041-022-09958-y}, eissn = {1531-5851}, issn = {1069-5869}, issue = {4}, journal = {Journal of Fourier Analysis and Applications}, publicationstatus = {Published}, publisher = {Springer}, url = {http://researchrepository.napier.ac.uk/Output/2965317}, volume = {28}, keyword = {Averages along curves, ℓp -improving, Diophantine equations}, year = {2022}, author = {Dendrinos, Spyridon and Hughes, Kevin and Vitturi, Marco} }