Space–time analytic smoothing effect of the heat semigroup defined on homogeneous Besov spaces

Partial Differential Equations in Applied Mathematics

卷:4

Taiki Takeuchi¹ 

[1] Department of Mathematics, Faculty of Science and Engineering, Waseda University, 3-4-1 Ookubo, Shinjuku-ku, Tokyo, 169-8555, Japan;

关键词: Heat semigroup;    Analyticity;    Homogeneous Besov spaces;    Fourier multiplier;   

DOI  :  

来源: DOAJ

【 摘 要 】

We refine the decay estimate of the heat semigroup {T(t)}t≥0defined on homogeneous Besov spaces Ḃp,qs(Rn)for s∈R,p,q∈[1,∞], which is obtained by Kozono et al. (2003). In particular, 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≥0is a bounded analytic C0-semigroup on Ḃp,qs(Rn)for s∈R,p,q∈[1,∞), where {T(t)}t≥0can be extended as an analytic function of t on the sector {t∈ℂ∖{0}||argt|<θ}with an explicitly given constant θ.

【 授权许可】

Unknown