Book:
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T.P. Hytönen, J.M.A.M. van Neerven, M.C. Veraar, L.W. Weis.
Analysis in Banach spaces Volume I: Martingales and Littlewood-Paley theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 2016 Volume II: Probabilistic Techniques and Operator Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 2017. Volume III: Harmonic Analysis and Spectral Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 2023. Comments and suggestions are welcome. |
Large deviations for stochastic evolution equations in the critical variational setting.
Counterexamples to maximal regularity for operators in divergence form.
Accepted for publication in Archiv der Mathematik
Strongly Kreiss Bounded Operators in UMD Banach Spaces.
An extrapolation result in the variational setting: improved regularity, compactness, and applications to quasilinear systems.
Temporal approximation of stochastic evolution equations with irregular nonlinearities.
To appear in Journal of Evolution equations
Pathwise Uniform Convergence of Time Discretisation Schemes for SPDEs.
Reaction-diffusion equations with transport noise and critical superlinear diffusion: Global well-posedness of weakly dissipative systems.
To appear in SIAM J. Math. Anal.
Reaction-diffusion equations with transport noise and critical superlinear diffusion: local well-posedness and positivity.
J. Differential Equations 368, (25), 2023, Pages 247-300
The critical variational setting for stochastic evolution equations.
Probab. Theory Related Fields 188 (2024), no. 3-4, 957–1015.
Higher order moments for SPDE with monotone nonlinearities.
Stochastic Navier-Stokes equations for turbulent flows in critical spaces.
Comm. Math. Phys. 405 (2024), no. 2, Paper No. 43, 57 pp.
Stochastic maximal Lp(Lq)-regularity for second order systems with periodic boundary conditions.
Ann. Inst. Henri Poincaré Probab. Stat. 60 (2024), no. 1, 413–430.
On the trace embedding and its applications to evolution equations.
Math. Nachr.2023;296:1319–1350.
Nonlinear parabolic stochastic evolution equations in critical spaces Part II.
Blow-up criteria and instantaneous regularization.
J. Evol. Equ. 22 (2022), no. 2, Paper No. 56.
Maximal estimates for stochastic convolutions in 2-smooth Banach spaces and applications to stochastic evolution equations.
Philosophical Transactions of the Royal Society A, 378(2185) (2020), 20190622.
Maximal inequalities for stochastic convolutions and pathwise uniform convergence of time discretisation schemes.
Stoch. Partial Differ. Equ. Anal. Comput. 10 (2022), no. 2, 516–581.
Nonlinear parabolic stochastic evolution equations in critical spaces Part I.
Stochastic maximal regularity and local existence.
Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence* 2022 IOP, Nonlinearity, Volume 35, Number 8
Extensions of the vector-valued Hausdorff-Young inequalities.
Mathematische Zeitschrift, 299(1), 373-425, 2021.
Singular stochastic integral operators.
Analysis and PDE Vol. 14 (2021), No. 5, 1443–1507.
Stability properties of stochastic maximal L^p-regularity.
J. Math. Anal. Appl. 482 (2020), no. 2, 123553. 60 (35)
On temporal regularity of stochastic convolutions in 2-smooth Banach spaces.
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Vol. 56(3), 2020, 1792–1808
The UMD property for Musielak--Orlicz spaces.
Positivity and Noncommutative Analysis. Festschrift in honour of Ben de Pagter on the occasion of his 65th birthday, Trends in Mathematics. Birkhäuser, 2019, 349-363.
Stochastic maximal regularity for rough time-dependent problems.
Stochastics and Partial Differential Equations: Analysis and Computations 7(4), 2019, 541–597.
The heat equation with rough boundary conditions and holomorphic functional calculus.
J. Differential Equations 269, (7), 2020, Pages 5832-5899.
Stochastic integration in quasi-Banach spaces.
Studia Math. 269 (2023), no. 1, 1–64.
Pointwise properties of martingales with values in Banach function spaces.
High Dimensional Probability VIII. The Oaxaca Volume. Progress in Probability 74, 2019. 321--340.
Sharp growth rates for semigroups using resolvent bounds.
J. Evol. Equ. 18 (2018), no. 4, 1721–1744.
Stability theory for semigroups using (L^p,L^q) Fourier multipliers.
J. Funct. Anal. 275 (2018), no. 10, 2845–2894.
Complex interpolation with Dirichlet boundary conditions on the half line.
Math. Nachr. 291 (2018), no. 16, 2435–2456.
Fourier multipliers in Banach function spaces with UMD concavifications.
Trans. Amer. Math. Soc. 371 (2019), no. 7, 4837–4868.
Rescaled extrapolation for vector-valued functions.
Publ. Mat. 63, Number 1 (2019), 155-182.
Fourier multiplier theorems on Besov spaces under type and cotype conditions.
Banach J. Math. Anal. Volume 11, Number 4 (2017), 713-743.
Fourier multiplier theorems involving type and cotype.
J Fourier Anal Appl (2018) 24:583–619.
Cylindrical continuous martingales and stochastic integration in infinite dimensions.
Electronic Journal of Probability. Volume 21, 2016
Regularity of stochastic Volterra equations by functional calculus methods.
J. Evol. Equ. 17 (2017), 523–536.
Evolution families and maximal regularity for systems of parabolic equations.
Adv. Differential Equations 22 (2017), no. 3-4, 169–190.
Estimates for vector-valued holomorphic functions and Littlewood-Paley-Stein theory.
Studia Math. 228 (1) (2015), 73-99.
On the $\ell^s$-boundedness of a family of integral operators.
Rev. Mat. Iberoam. 32 (2016), no. 4, 1277–1294.
Maximal regularity for non-autonomous equations with measurable dependence on time.
Potential Analysis 46 (2017), 527–567.
Characterization of a class of embeddings for function spaces with Muckenhoupt weights.
Arch. Math. 103 (2014), 435–449.
R-boundedness versus gamma-boundedness.
Arkiv för Matematik, 54(1) (2016), 125-145.
On the R-boundedness of stochastic convolution operators.
Positivity. 19 (2015), no. 2, 355-384.
A new approach to stochastic evolution equations with adapted drift.
J. Differential Equations 256 (2014), no. 11, 3634–3683.
Pointwise multiplication on vector-valued function spaces with power weights.
J. Fourier Anal. Appl. 21 (2015), no. 1, Page 95-136.
Forward integration, convergence and nonadapted pointwise multipliers.
Infin. Dimens. Anal. Quantum Probab. Relat. Top. 18, No. 1 (2015).
Stochastic integration in Banach spaces -- a survey.
Published in the proceedings of the 2012 EPFL Semester on Stochastic Analysis and Applications.
Maximal regularity in gamma-spaces.
J. Evol. Equ. 2015, 15 (2015), no. 2, 361-402.
Traces and embeddings of anisotropic function spaces.
Math. Ann. 360 (2014), No 3-4, 571–606.
Weak characterizations of stochastic integrability and Dudley's theorem in infinite dimensions.
J. Theoret. Probab. 27, No. 4, (2014) 1350-1374.
Tools for Malliavin calculus in UMD Banach spaces.
Potential Anal. 40, No. 4 (2014), 307-344.
Embedding results for gamma-spaces.
Recent trends in analysis. Proceedings of the conference in honor of Nikolai Nikolski on the occasion of his 70th birthday, Bordeaux, France. Bucharest: The Theta Foundation (ISBN 978-606-8443-02-7). Theta Series in Advanced Mathematics, 209-219 (2013)
Sharp embedding results for spaces of smooth functions with power weights.
Studia Math. 208 (2012), 257-293.
Is the stochastic parabolicity condition dependent on $p$ and $q$?.
Electron. J. Probab. 17, article 56 (2012).
Regularity of Gaussian white noise on the d-dimensional torus.
Proceedings of the Józef Marcinkiewicz centenary conference. Banach Center Publ. 95 (2011), 385-398.
Maximal Lp-regularity for stochastic evolution equations.
SIAM J. Math. Anal. 44 (3), 1372-1414.
The stochastic Fubini theorem revisited.
Stochastics Vol. 84 issue 4 (2012) 543-551.
A note on maximal estimates for stochastic convolutions.
Czechoslovak Math. J. 61 (136) (2011), 743–758.
Stochastic maximal Lp-regularity.
Annals Probab. Vol. 40 (2012), No. 2, 788–812.
Stochastic equations with boundary noise.
In: Nonlinear Parabolic Problems: Herbert Amann Festschrift
Progress in Nonlinear Differential Equations and Their Applications, Vol. 60, Birkhäuser Verlag, 2011.
On Khintchine inequalities with a weight.
Proc. Amer. Math. Soc. 138 (2010), Nr. 11, 4119–4121.
Vector-valued decoupling and the Burkholder-Davis-Gundy inequality.
Illinois J. Math. 55 (2011), Nr. 1, 343–375.
On semi-R-boundedness and its applications.
J. Math. Anal. Appl. 363 (2010), Nr. 2, 431-443.
Structurally damped plate and wave equations with random point force in arbitrary space dimensions.
Differential and Integral Equations. 23, Nr. 9-10 (2010), 957-988.
Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations.
J. Evol. Equ. 10 (2010), 85–127 (Open Acces).
Nemirovski's Inequalities Revisited.
Amer. Math. Monthly (Februari, 2010).
R-boundedness of smooth operator-valued functions.
Integral Eq. Operator Th. 63 (2009), 373-402.
Correlation inequalitites and applications to vector-valued Gaussian random variables and fractional Brownian motion.
Potential Anal. 30, No. 4 (2009), 341-370.
A note on optimal probability lower bounds for centered random variables.
Colloq. Math. 113, No. 2, 231-240 (2008).
Some remarks on tangent martingale difference sequences in L^1 spaces.
Electron. Commun. Probab. 12, 421-433, electronic only (2007).
On Besov regularity of Brownian motions in infinite dimensions.
Probab. Math. Statist 28, No. 1, 143-162 (2008).
Conditions for stochastic integrability in UMD Banach spaces.
In: Banach Spaces and their Applications in Analysis (in Honor of Nigel Kalton's 60th Birthday)
De Gruyter Proceedings in Mathematics, De Gruyter, 2007
Embedding vector-valued Besov spaces into spaces of gamma-radonifying operators
Math. Nachr. 281, No. 2, 238-252 (2008).
A stochastic Datko-Pazy theorem
J. Math. Anal. Appl. 329 (2007), 1230-1239
Ito's formula in UMD Banach spaces and regularity of solution of the Zakai equation,
J. Differ. Equations 245, No. 1, 30-58 (2008).
Stochastic evolution equations in UMD Banach spaces,
J. Funct. Anal. 255, No. 4, 940-993 (2008).
Continuous local martingales and stochastic integration in UMD Banach spaces.
Stochastics Vol. 79 issue 6 (2007) 601-618.
Non-autonomous stochastic Cauchy problems in Banach spaces.
Stud. Math. 185, No. 1, 1-34 (2008).
Stochastic integration in UMD Banach spaces
Annals Probab. 35 (2007), 1438-1478
MR 2 330 977
Randomized UMD Banach Spaces and Decoupling Inequalities for Stochastic Integrals
Proc. Amer. Math. Soc. 135 (2007), 1477-1486.
On the action of Lipschitz functions on vector-valued random sums
Archiv Math. 85 (Basel) (2005) - 544-553.
On the stochastic Fubini theorem in infinite dimensions
In: "Stochastic Partial Differential Equations and Applications - VII" (Levico Terme, 2004), Lecture Notes in Pure and Applied Mathematics, Volume 245, CRC Press, 2005.