K. Bogdan, T. Byczkowski, T. Kulczycki, M. Ryznar, R. Song, Z. Vondracek, “Potential Analysis of Stable Processes and its Extensions”, Lecture Notes in Mathematics 1980, Springer, Berlin (2009).


1.      S. Jarohs, T. Kulczycki, P. Salani, “On the Bernoulli free boundary problems for the half Laplacian and for the spectral half Laplacian”, Nonlinear Anal. 222 (2022), Paper No. 112956, 39 pp.

2.      T. Kulczycki, A. Kulik, M. Ryznar, “On weak solution of SDE driven by inhomogeneous singular Lévy noise”, Trans. Amer. Math. Soc. 375 (2022), 4567-4618.

3.      T. Kulczycki, M. Ryznar, P. Sztonyk, “Strong Feller property for SDEs driven by multiplicative cylindrical stable noise”, Potential Analysis 55 (2021), 75-126.

4.      T. Kulczycki, M. Ryznar, “Semigroup properties of solutions of SDEs driven by Lévy processes with independent coordinates”, Stoch. Proc. Appl. 130 (2020) 7185-7217..

5.      S. Jarohs, T. Kulczycki, P. Salani, “Starshape of the superlevel sets of solutions to equations involving the fractional Laplacian in starshaped rings”, Mathematische Nachrichten 292 (2019), 1008-1021.

6.      T. Kulczycki, M. Ryznar, “Transition density estimates for diagonal systems of SDEs driven by cylindrical α-stable processes”, ALEA Lat. Am. J. Probab. Math. Stat. 15 (2018), 1335-1375.

7.      T. Kulczycki, M. Ryznar, “Gradient estimates of Dirichlet heat kernels for unimodal Lévy processes”, Mathematische Nachrichten 291 (2018), 374-397.

8.      T. Kulczycki, “On concavity of solutions of the Dirichlet problem for the equation (-Δ)1/2 φ = 1 in convex planar regions”, Journal of the European Mathematical Society 19 (2017), 1361-1420.

9.      T. Kulczycki, “Mid-concavity of survival probability for isotropic Lévy processes”, Electron. Commun. Probab. 21 (2016), no. 29, 1-9.

10.  T. Kulczycki, M. Ryznar, “Gradient estimates of harmonic functions and transition densities for Levy processes”, Trans. Amer. Math. Soc., 368 (2016), no. 1, 281–318.

11.  T. Kulczycki, M. Kwaśnicki, B. Siudeja, “On the shape of the fundamental sloshing mode in axisymmetric containers”, Journal of Engineering Mathematics 99 (2016), 157-183.

12.  T. Kulczycki, R. Stańczy, “Multiple solutions for Dirichlet nonlinear BVPs involving fractional Laplacian”, Discrete Contin. Dyn. Syst. Ser. B 19 (2014), 2581-2591.

13.  N. Kuznetsov, T. Kulczycki, M.  Kwaśnicki, A. Nazarov, S. Poborchi, I. Polterovich, B. Siudeja, “The legacy of Vladimir Andreevich Steklov”, Notices Amer. Math. Soc. 61 (2014),  9–22.

14.  K. Burdzy, T. Kulczycki,  “Invisibility via reflecting coating”, J. London Math. Soc. 88 (2013), 359-374.

15.  T. Kulczycki,  “Gradient estimates of q-harmonic functions of fractional Schrödinger operator”,  Potential Analysis 39 (2013), 69–98.  

16.    K. Burdzy, T. Kulczycki, R. Schilling,  ”Stationary distributions for jump processes with inert drift”,   in “Malliavin Calculus and Stochastic Analysis: A Festschrift in Honor of David Nualart”, Springer Proceedings in Mathematics & Statistics 34, Springer Science+Business Media New York (2013), 139-172.

17.   T. Kulczycki, M. Kwaśnicki,  ”On high spots of the fundamental sloshing eigenfunctions in axially symmetric domains”,   Proc. London Math. Soc. 105 (2012),  921-952.

18.   K. Burdzy, T. Kulczycki, R. Schilling, "Stationary distributions for jump processes with memory" Ann. Inst. Henri Poincaré Probab. Stat.  48 (2012), 609–630.

19.   T. Kulczycki, N. Kuznetsov, “On the ‘high spots’ of fundamental sloshing modes in a trough”, Proc. Roy. Soc. London Ser. A  467 (2011), 1491-1502.

20.    R. Bañuelos, T. Kulczycki, I. Polterovich, B. Siudeja, “Eigenvalue inequalities for mixed Steklov problems”,  Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008), Advances in the Mathematical Sciences, AMS Translations 231, (2010), pp. 19-34.

21.   K. Kaleta, T. Kulczycki, ”Intrinsic ultracontractivity for Schrödinger operators based on fractional Laplacians”, Potential Analysis 33 (2010), 313-339 .

22.    T. Kulczycki, M. Kwaśnicki, J. Małecki, A. Stós, ”Spectral properties of the Cauchy process on half-line and interval”, Proc. London. Math. Soc. 101 (2010), 589-622.

23.   R. Bañuelos, T. Kulczycki, B. Siudeja, “On the trace of symmetric stable processes on Lipschitz domains”, J. Funct. Anal. 257 (2009), no. 10, 3329-3352.

24.   T. Kulczycki, N. Kuznetsov, “’High spots' theorems for sloshing problems”, Bull. Lond. Math. Soc. 41 (2009), 495-505.

25.   R. Bañuelos, T. Kulczycki, B. Siudeja, “Neumann Bessel Heat Kernel Monotonicity”, Potential Anal. 30 (2009), no. 1, 65-83.

26.   R. Bañuelos, T. Kulczycki, “Trace estimates for stable processes”,  Probab. Theory Relat. Fields 142 (2008), 313-338.

27.   K. Bogdan, T. Kulczycki, M. Kwaśnicki, “Estimates and structure of  α-harmonic functions”, Probab. Theory Relat. Fields140 (2008), 345-381.

28.   B. Dyda, T. Kulczycki, “Spectral gap for stable process on convex double symmetric domains”, Potential Anal. 27 (2007), 101-132.

29.   R. Bañuelos, T. Kulczycki,  „Spectral gap for the Cauchy process on convex, symmetric domains”,  Comm. Partial Differential Equations 31 (2006), 1841–1878.

30.   R. Bañuelos, T. Kulczycki, P. Mendez-Hernandez,  „On the shape of the ground state eigenfunction for stable processes”, Potential Anal. 24 (2006), 205-221.

31.   R. Bañuelos, T. Kulczycki,  „Eigenvalue gaps for the Cauchy process and a Poincare inequality”, J. Funct. Anal 234 (2006), 199-225.

32.   T. Kulczycki, B. Siudeja,  „Intrinsic ultracontractivity of Feynman-Kac semigroup for relativistic stable processes”,  Trans. Amer. Math. Soc. 358(11) (2006), 5025--5057.

33.   R. Bañuelos, T. Kulczycki, “The Cauchy process and the Steklov problem” J. Funct. Anal. 211 (2004), no. 2, 355--423.

34.   K. Burdzy, T. Kulczycki, “Stable processes have thorns” Ann. Probab. 31 (2003), no. 1, 170--194.

35.   K. Bogdan, T. Kulczycki, A. Nowak, “Gradient estimates for harmonic and $q$-harmonic functions of symmetric stable processes” Illinois J. Math. 46 (2002), no. 2, 541--556.

36.   T. Kulczycki, “Exit time and Green function of cone for symmetric stable processes” Probab. Math. Statist. 19 (1999), no. 2, 337--374.

37.   T. Kulczycki, “Intrinsic ultracontractivity for symmetric stable processes” Bull. Polish Acad. Sci. Math. 46 (1998), no. 3, 325--334.

38.   T. Kulczycki “Properties of Green function of symmetric stable processes” Probab. Math. Statist. 17 (1997), no. 2, 339--364.