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BOUNDED H1-CALCULUS FOR ELLIPTIC OPERATORS Herbert Amann and Matthias Hieber
 

Summary: BOUNDED H1-CALCULUS FOR ELLIPTIC OPERATORS
Herbert Amann and Matthias Hieber
Math. Institut, Universitat Zurich, Winterthurerstr. 190, CH{8057 Zurich, Switzerland
Gieri Simonett
Department of Mathematics, UCLA, 405 Hilgard Ave., Los Angeles, CA90024{1555, USA
In memoriam Peter Hess
Abstract. It is shown, in particular, that Lp -realizations of general elliptic systems on R n
or on compact manifolds without boundaries possess bounded imaginary powers, provided
rather mild regularity conditions are satis ed. In addition, there are given some new per-
turbation theorems for operators possessing a bounded H1 -calculus.
0. Introduction. It is the main purpose of this paper to prove | under mild
regularity assumptions | that L p -realizations of elliptic di erential operators act-
ing on vector valued functions over R n or on sections of vector bundles over com-
pact manifolds without boundaries possess bounded imaginary powers. In fact, we
shall prove a more general result guaranteeing that, given any elliptic operator A
with a suÆciently large zero order term such that the spectrum of its principal
symbol is contained in a sector of the form S 0 := f z 2 C ; j arg zj   0 g [ f0g for
some  0 2 [0; ), and given any bounded holomorphic function f :
Æ
S  ! C for some

  

Source: Amann, Herbert - Institut für Mathematik, Universität Zürich

 

Collections: Mathematics