Unique continuation for the heat operator with potentials in weak spaces

We prove the strong unique continuation property for the differential inequalitywith V contained in weak spaces.In particular, we establish the strong unique continuation property for, which has been left open since the works of Escauriaza ( 2000) and Escauriaza and Vega (2001).Our results are consequences of the Carleman estimates for the heat operator in the Lorentz spaces.d/2 loc , d ≥ 3. Their result was extended by