A counterexample to the global dual L3 Schrodinger maximal estimate in R2

In this paper, we give an elementary counterexample to show that the global L-3 Schrodinger maximal estimate vertical bar vertical bar sup (0<|t|<= 1) |e(it Delta) f| vertical bar vertical bar(L3(R2)) <= C vertical bar vertical bar f vertical bar vertical bar(Hs(R2)), for all f is an element of H-s(R-2) fails if s < 1/3. The argument also adapts to the case of 2D fractional Schrodinger operators, and does not rely on any facts from number theory. (c) 2023 Elsevier Inc. All rights reserved.

Automated summary

In this paper, an elementary counterexample is given to show that the global L-3 Schrodinger maximal estimate fails if s < 1/3. The argument also applies to the case of 2D fractional Schrodinger operators and does not rely on any facts from number theory.