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Department of Mathematics

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Institutes

Institute for Analysis

Workgroup Functional Analysis

Prof. Dr. Lutz Weis

Prof. Dr. Lutz Weis

Photo of Lutz Weis

Prof. Dr. Lutz Weis

$Office hour for students$
$Building$ Kollegiengebäude Mathematik (20.30)
$Room$ 2.047
$Tel.$ +49 721 608 43821
$Fax$ +49 721 608 46177
lutz.weis@kit.edu

Karlsruher Institut für Technologie
Fakultät für Mathematik
Institut für Analysis
Englerstrasse 2
76131 Karlsruhe
Germany

Welcome on the homepage of Lutz Weis

Research

Areas of research

Functional analysis and its applications to partial differential equations.
Operator semigroups and its applications to Stability and Regularity of the Cauchy problem.
Spectral theory, in particular $H^\infty$ -calculus for sectorial operators.
Vectorvalued harmonic analysis and its connection with Geometry of Banach spaces.
Stochastic Evolution Equations with infinite-dimensional state space.

Selected publications

Books and Book chapters

Tuomas Hytönen, Jan van Neerven, Mark Veraar, and Lutz Weis, Analysis in Banach Spaces (in preparation)

Peer C. Kunstmann and Lutz Weis, Maximal $L_p$ -regularity for parabolic equations, Fourier multiplier theorems and $H^\infty$ -functional calculus, Functional analytic methods for evolution equations, Lecture Notes in Math., vol. 1855, Springer, Berlin, 2004, pp.~65--311.

Günter Lumer and Lutz Weis (eds.), Evolution equations and their applications in physical and life sciences, Lecture Notes in Pure and Applied Mathematics, vol. 215, New York, Marcel Dekker Inc., 2001.

Recent Articles

Jan van Neerven, Mark Veraar, and Lutz Weis, Stochastic maximal $L_p$ -regularity, Annals of Probability,(to appear).

Jan van Neerven, Mark Veraar, and Lutz Weis, Maximal $L^p$ -regularity for stochastic evolution equations, SIAM Journal on Mathematical Analysis, (to appear).

Mark Veraar and Lutz Weis, A note on maximal estimates for stochastic convolutions, Czechoslovak Math. J. 61 (2011), no. 3, 743-758.

Jan van Neerven and Lutz Weis, Vector measures of bounded $\gamma$ -variation and stochastic integrals, Vector measures, integration and related topics, Oper. Theory Adv. Appl., vol. 201, Birkhäuser Verlag, Basel, 2010, pp. 303-311.

Christoph Kriegler and Lutz Weis, Contractivity of the $H^\infty$ -calculus and Blaschke products, Operator algebras, operator theory and applications, Oper. Theory Adv. Appl., vol. 195, Birkhäuser Verlag, Basel, 2010, pp. 231-244.

Tuomas P. Hytönen and Lutz Weis, The Banach space-valued BMO, Carleson's condition, and paraproducts, J. Fourier Anal. Appl. 16 (2010), no. 4, 495-513.

Mark Veraar and Lutz Weis, On semi- $\mathcal{R}$ -boundedness and its applications, J. Math. Anal. Appl. 363 (2010), no. 2, 431-443.

Jesus Suarez and Lutz Weis, Addendum to ´Interpolation of Banach spaces by the $\gamma$ -method´, Extracta Math. 24(2009), no. 3, 265-269.

J. M. A. M. van Neerven, M. C. Veraar, and L. Weis, Stochastic evolution equations in UMD Banach spaces, J. Funct. Anal. 255(2008), no. 4, 940-993.

J. M. A. M. van Neerven and L. Weis, Stochastic integration of operator-valued functions with respect to Banach space-valued Brownian motion, Potential Anal. 29 (2008), no. 1, 65-88.

Z. Brzezniak, J. M. A. M. van Neerven, M. C. Veraar, and L. Weis, Ito's formula in UMD Banach spaces and regularity of solutions of the Zakai equation, J. Differential Equations 245 (2008), no. 1, 30-58.

Cornelia Kaiser and Lutz Weis, Wavelet transform for functions with values in UMD spaces, Studia Math. 186 (2008), no. 2, 101-126.

Nigel Kalton, Jan van Neerven, Mark Veraar, and Lutz Weis, Embedding vector-valued Besov spaces into spaces of $\gamma$ -radonifying operators, Math. Nachr. 281 (2008), no. 2, 238-252.

J. van Neerven, M. Veraar and L. Weis, Stochastic integration in UMD Banach spaces, Ann. Prob. 35 (2007), No. 4, 1438-1478.

A. Fröhlich and L. Weis, $H^\infty$ -calculus and dilations, Bull. Soc. Math. France 134 (2006), No. 4, 485-506.

T. Hytoenen and L. Weis, Singular convolution integrals with operator-valued kernels, Math. Zeit. 255 (2007), No. 2, 393-425.

Z. Strkalj and L. Weis, On operator-valued Fourier multiplier theorems, Trans. Am. Math. Soc. 359 (2007), No. 8, 3529-3547.

T. Hytoenen and L. Weis, A $T1$ theorem for integral transformations with operator-valued kernel, J. Reine Angew. Math. 599 (2006), 155-200.

N. J. Kalton, P. C. Kunstmann and L. Weis, Perturbation and interpolation results for the $H^\infty$ -calculus with applications to partial differential equations, Math. Ann. 336 (2006), No. 4, 747-801.

T. Hytoenen and L. Weis, Singular integrals on Besov space, Math. Nachr. 279 (2006), No. 5-6, 581-598.

J. Dettweiler, L. Weis and J. van Neerven, Space-time regularity of solutions of the parabolic stochastic Cauchy problem, Stoch. Anal. Appl. 24 (2006), No. 4, 843-869.

J.M.A.M. van Neerven and L. Weis, Invariant measures for the linear stochastic Cauchy problem and $R$ -boundedness of the resolvent, J. Evol. Equ. 6 (2006), No. 2, 205-228.

J.M.A.M. van Neerven and L. Weis, Stochastic integration of functions with values in a Banach space, Studia Math. 166 (2005), No. 2, 131-170.

J.M.A.M. van Neerven and L. Weis, Weak limits and integrals of Gaussian covariances in Banach spaces, Probab. Math. Statist. 25 (2005), No. 1, 55-74.

T. Kucherenko and L. Weis, Real interpolation of domains of sectorial operators on $L_p$ -spaces, J. Math. Anal. Appl. 310 (2005), No. 1, 278-285.

M. Girardi and L. Weis, Operator-valued martingale transforms and $R$ -boundedness, Illinois J. of Math. 49 (2005), No. 2, 487-516 (electronic).