#### Vol. 11, No. 3, 2018

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The semigroup generated by the Dirichlet Laplacian of fractional order

### Tsukasa Iwabuchi

Vol. 11 (2018), No. 3, 683–703
##### Abstract

In the whole space ${ℝ}^{d}$, linear estimates for heat semigroup in Besov spaces are well established, which are estimates of ${L}^{p}-{L}^{q}$ type, with maximal regularity, etc. This paper is concerned with such estimates for the semigroup generated by the Dirichlet Laplacian of fractional order in terms of the Besov spaces on an arbitrary open set of ${ℝ}^{d}$.

##### Keywords
semigroup, Dirichlet Laplacian, Besov spaces
Primary: 35R11
Secondary: 35K08
##### Milestones
Received: 4 January 2017
Revised: 30 August 2017
Accepted: 16 October 2017
Published: 22 November 2017
##### Authors
 Tsukasa Iwabuchi Mathematical Institute Tohoku University Sendai Japan