| 概要 |
We refine the decay estimate of the heat semigroup {𝑇(𝑡)}_<𝑡≥0> defined on homogeneous Besov spaces for Ḃ^𝑠 _<𝑝,𝑞> (R^𝑛) for 𝑠 ∈ R, 𝑝, 𝑞 ∈ [1, ∞], which is obtained by Kozono et al. (2003). In particu...lar, we give an explicit representation of a constant appeared in the decay estimate of {𝑇(𝑡)}_<𝑡≥0>, which provides a space–time analytic smoothing effect of {𝑇(𝑡)}_<𝑡≥0>. As a by-product, we obtain a radius of convergence of the Taylor expansion exactly. Furthermore, it is also showed that {𝑇(𝑡)}_<𝑡≥0> is a bounded analytic 𝐶_0-semigroup on Ḃ^𝑠 _<𝑝,𝑞> (R^𝑛) for 𝑠 ∈ R, 𝑝, 𝑞 ∈ [1, ∞] , where {𝑇(𝑡)}_<𝑡≥0> can be extended as an analytic function of on the sector {𝑡 ∈ C ⧵ {0} | | arg 𝑡| < 𝜃} with an explicitly given constant .続きを見る
|
Mendeley出力
2021PADIFF-T-Heatsemi