Phases of unimodular complex valued maps: optimal estimates, the factorization method, and the sum-intersection property of Sobolev spaces

摘要

We address and answer the question of optimal lifting estimates for unimodular complex valued maps: given s > 0 and 1 < p < co, find the best possible estimate of the form broken vertical bar phi broken vertical bar W-s,W-p less than or similar to F (broken vertical bar e(I phi)broken vertical bar W-s,W-p).