22 research outputs found
The -boundedness of a family of integral operators on UMD Banach function spaces
We prove the -boundedness of a family of integral operators with an
operator-valued kernel on UMD Banach function spaces. This generalizes and
simplifies earlier work by Gallarati, Veraar and the author, where the
-boundedness of this family of integral operators was shown on Lebesgue
spaces. The proof is based on a characterization of -boundedness as
weighted boundedness by Rubio de Francia.Comment: 13 pages. Generalization of arXiv:1410.665
Maximal regularity for non-autonomous equations with measurable dependence on time
In this paper we study maximal -regularity for evolution equations with
time-dependent operators . We merely assume a measurable dependence on time.
In the first part of the paper we present a new sufficient condition for the
-boundedness of a class of vector-valued singular integrals which does not
rely on H\"ormander conditions in the time variable. This is then used to
develop an abstract operator-theoretic approach to maximal regularity.
The results are applied to the case of -th order elliptic operators
with time and space-dependent coefficients. Here the highest order coefficients
are assumed to be measurable in time and continuous in the space variables.
This results in an -theory for such equations for .
In the final section we extend a well-posedness result for quasilinear
equations to the time-dependent setting. Here we give an example of a nonlinear
parabolic PDE to which the result can be applied.Comment: Application to a quasilinear equation added. Accepted for publication
in Potential Analysi
On the existence of mild solutions to the Cauchy problem for a class of fractional evolution equation
Backward Stochastic Evolution Equations in UMD Banach Spaces
Extending results of Pardoux–Peng and Hu–Peng, we prove well-posedness results for backward stochastic evolution equations in UMD Banach spaces.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Analysi
The â„“ <sup>s</sup>-boundedness of a family of integral operators on UMD banach function spaces
We prove the â„“s-boundedness of a family of integral operators with an operator-valued kernel on UMD Banach function spaces. This generalizes and simplifies earlier work by Gallarati, Veraar and the author, where the â„“s-boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a characterization of â„“s-boundedness as weighted boundedness by Rubio de Francia.Analysi