A comment on an $L^{\frac{2n}{n+2}}-L^{\frac{2n}{n-2}}$ Carleman inequality in relation to "the determination of an unbounded potential from Cauchy data"

The proof of \cite[Proposition 2.1]{DKS}[arXiv:1104.0232] is partially incorrect. In this short note, we provide a new proof, which requires an additional hypothesis. A modification of this new proof also corrects the proof of \cite[Proposition 2.1]{Ch}[arXiv:2310.17456], where the incorrect argument of \cite{DKS} has been repeated.