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The semigroup generated by the Dirichlet Laplacian of fractional order (1712.05565v1)

Published 15 Dec 2017 in math.AP

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