Semigroups generated by certain pseudo-differential operators on the half-space $ℝ_{0+}^{n+1}$

Victoria Knopova

Semigroups generated by certain pseudo-differential operators on the half-space

ℝ_{0 +}^{n + 1}

Victoria Knopova

Colloquium Mathematicae, Tome 100 (2004), p. 221-236 / Harvested from The Polish Digital Mathematics Library

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Résumé

The aim of the paper is two-fold. First, we investigate the ψ-Bessel potential spaces on $ℝ_{0 +}^{n + 1}$ and study some of their properties. Secondly, we consider the fractional powers of an operator of the form $- A_{\pm} = - ψ (D_{x^{'}}) \pm \partial / (\partial x_{n + 1})$ , $(x^{'}, x_{n + 1}) \in ℝ_{0 +}^{n + 1}$ , where $ψ (D_{x^{'}})$ is an operator with real continuous negative definite symbol ψ: ℝⁿ → ℝ. We define the domain of the operator $- {(- A_{\pm})}^{α}$ and prove that with this domain it generates an $L_{p}$ -sub-Markovian semigroup.

Publié le : 2004-01-01

Zbl 1071.47046

EUDML-ID : urn:eudml:doc:283642

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     author = {Victoria Knopova},
     title = {Semigroups generated by certain pseudo-differential operators on the half-space $$\mathbb{R}$\_{0+}^{n+1}$
            },
     journal = {Colloquium Mathematicae},
     volume = {100},
     year = {2004},
     pages = {221-236},
     zbl = {1071.47046},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm101-2-6}
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Victoria Knopova. Semigroups generated by certain pseudo-differential operators on the half-space $ℝ_{0+}^{n+1}$
            . Colloquium Mathematicae, Tome 100 (2004) pp. 221-236. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm101-2-6/