On the $\Cal L$-characteristic of fractional powers of linear operators

Jürgen Appell; Marilda A. Simões; Petr P. Zabrejko

Displaying similar documents to “On the $\Cal L$-characteristic of fractional powers of linear operators”

Fractional powers of non-densely defined operators

Celso Martinez, Miguel Sanz (1991)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Distributional fractional powers of the Laplacean. Riesz potentials

Celso Martínez, Miguel Sanzi, Francisco Periago (1999)

Studia Mathematica

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For different reasons it is very useful to have at one’s disposal a duality formula for the fractional powers of the Laplacean, namely, $({(- Δ)}^{α} u, ϕ) = (u, {(- Δ)}^{α} ϕ)$ , α ∈ ℂ, for ϕ belonging to a suitable function space and u to its topological dual. Unfortunately, this formula makes no sense in the classical spaces of distributions. For this reason we introduce a new space of distributions where the above formula can be established. Finally, we apply this distributional point of view on the fractional powers of...

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R. Seeley (1972)

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The Sobolev-Besov imbedding theorem from the viewpoint of semi-groups of operators

H. Komatsu (1972-1973)

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A functional calculus description of real interpolation spaces for sectorial operators

Markus Haase (2005)

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For a holomorphic function ψ defined on a sector we give a condition implying the identity ${(X, (A^{α}))}_{θ, p} = x \in X | t^{- θ R e α} ψ (t A) \in L ⁎^{p} ((0, \infty); X)$ where A is a sectorial operator on a Banach space X. This yields all common descriptions of the real interpolation spaces for sectorial operators and allows easy proofs of the moment inequalities and reiteration results for fractional powers.

Real interpolation and compactness.

Fernando Cobos Díaz (1989)

Revista Matemática de la Universidad Complutense de Madrid

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The behavior of compactness under real interpolation real is discussed. Classical results due to Krasnoselskii, Lions-Peetre, Persson, and Hayakawa are described, as well as others obtained very recently by Edmunds, Potter, Fernández, and the author.

Fractional powers of non-negative operators in Fréchet spaces.

Martinez, C., Sanz, M., Calvo, V. (1989)

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A commutator theorem with applications.

Mario Milman (1993)

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We give an extension of the commutator theorems of Jawerth, Rochberg and Weiss [9] for the real method of interpolation. The results are motivated by recent work by Iwaniek and Sbordone [6] on generalized Hodge decompositions. The main estimates of these authors are based on a commutator theorem for a specific operator acting on Lp spaces and through the use of the complex method of interpolation. In this note we give an extension of the Iwaniek-Sbordone theorem to general real interpolation...