An optimal time-singularity of the estimate for the heat semigroup related to the critical Sobolev embedding

Yi C. Huang, Tohru Ozawa, Chenmin Sun +1

We give a certain $L^{\infty }({\mathbb{R}}^2)$-estimate for the heat semigroup $\{e^{t\Delta }{\}}_{t\ge 0}$ that is closely related to the fact $H^1(\mathbb{R}^2) \not\subset L^{\infty}(\m…