The permanence of R-boundedness and property(alpha) under interpolation and applications to parabolic systems

Saal, Jürgen; Kaip, Mario

The permanence of R-boundedness and property(alpha) under interpolation and applications to parabolic systems

Publikationstyp:	Preprint
URI (zitierfähiger Link):	http://nbn-resolving.de/urn:nbn:de:bsz:352-165994
Autor/innen:	Saal, Jürgen; Kaip, Mario
Erscheinungsjahr:	2011
Schriftenreihe:	Konstanzer Schriften in Mathematik ; 290
Zusammenfassung:	This note consists of two parts. In the first part we consider the behavior of R-boundedness, R-sectoriality, and property(α) under the interpolation of Banach spaces. In a general setting we prove that for interpolation functors of type h the R-boundedness, the R-sectoriality, and the property(α) preserve under interpolation. In particular, this is true for the standard real and complex interpolation methods. The second part represents an application of the first part. We prove R-sectoriality, or equivalently, maximal Lp-regularity for a general class of parabolic systems on interpolation spaces including scales of Besov- and Bessel-potential spaces over Rn.
MSC-Klassifikation:	Primary 46B70, 47F05; Secondary 35K41, 35K46
Fachgebiet (DDC):	510 Mathematik
Normierte Schlagwörter (GND):	System von partiellen Differentialgleichungen
Schlagwörter:	Interpolation von Banachräumen, R-Beschränktheit, maximale Regularität, parabolische Systeme
Link zur Lizenz:	Deposit-Lizenz
Universitätsbibliographie:	Ja

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SAAL, Jürgen, Mario KAIP, 2011. The permanence of R-boundedness and property(alpha) under interpolation and applications to parabolic systems

@unpublished{Saal2011perma-16599, title={The permanence of R-boundedness and property(alpha) under interpolation and applications to parabolic systems}, year={2011}, author={Saal, Jürgen and Kaip, Mario} }

2011-11-15T10:26:42Z 2011-11-15T10:26:42Z 2011 eng Kaip, Mario deposit-license Saal, Jürgen Saal, Jürgen The permanence of R-boundedness and property(alpha) under interpolation and applications to parabolic systems This note consists of two parts. In the first part we consider the behavior of R-boundedness, R-sectoriality, and property(α) under the interpolation of Banach spaces. In a general setting we prove that for interpolation functors of type h the R-boundedness, the R-sectoriality, and the property(α) preserve under interpolation. In particular, this is true for the standard real and complex interpolation methods. The second part represents an application of the first part. We prove R-sectoriality, or equivalently, maximal Lp-regularity for a general class of parabolic systems on interpolation spaces including scales of Besov- and Bessel-potential spaces over Rn. Kaip, Mario