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

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Knopova V.

Colloquium Mathematicum

2004

tom 101

nr 2

221-236

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 $-A_± = -ψ(D_{x'}) ± ∂/(∂x_{n+1})$, $(x',x_{n+1}) ∈ ℝ^{n+1}_{0+}$, where $ψ(D_{x'})$ is an operator with real continuous negative definite symbol ψ: ℝⁿ → ℝ. We define the domain of the operator $-(-A_±)^{α}$ and prove that with this domain it generates an $L_{p}$-sub-Markovian semigroup.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Knopova V.

1 2004

Wyniki wyszukiwania

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