Generalizations of the Schrödinger maximal operator: building arithmetic counterexamples

Rena Chu, Lillian B. Pierce

Let $T_t^{P_2}f(x)$ denote the solution to the linear Schrödinger equation at time $t$, with initial value function $f$, where $P_2(\xi )=|\xi {|}^2$. In 1980, Carleson asked for the mi…