Publications of Piotr Hajlasz

2017 and later

[1] P. Goldstein, P. Hajlasz, M. R. Pakzad, On regularity of second order Sobolev isometric immersions. (In preparation.)
[2] D. Azagra, P. Hajlasz, Lusin-type properties of convex functions. (In preparation.)
[3] M. Bownik, P. Hajlasz, F. L. Nazarov, P. Wojtaszczyk, Translation invariant operators on $L^\infty$. (Preprint.)
[4] P. Hajlasz, B. Esmayli, A new proof of the Freudenthal suspension theorem. (Preprint.)
[5] P. Goldstein, P. Hajlasz, M. R. Pakzad, Finite distortion Sobolev mappings between manifolds are continuous. (Submitted.)
[6] P. Hajlasz, S. Malekzadeh, S. Zimmerman, Weak BLD mappings and Hausdorff measure (Submitted.) arXiv
[7] P. Goldstein, P. Hajlasz, Modulus of continuity of orientation preserving approximately differentiable homeomorphisms with a.e. negative Jacobian. (Submitted.) arXiv
[8] P. Hajlasz, The (n+1)-Lipschitz homotopy group of the Heisenberg group Hn. Proc. Amer. Math. Soc. (To appear.) arXiv
[9] P. Hajlasz, S. Zimmerman, Dubovitskij-Sard theorem for Sobolev mappings. Indiana Univ. Math. J. 66 (2017), 705-723. arXiv
[10] P. Goldstein, P. Hajlasz, A measure and orientation preserving homeomorphism of a cube with Jacobian equal $-1$ almost everywhere. Arch. Ration. Mech. Anal. 225 (2017), 65-88. arXiv
[11] P. Hajlasz, Z. Liu, A Marcinkiewicz integral type characterization of the Sobolev space. Publ. Mat. Publ. Mat. 61 (2017), 83--104. arXiv
[12] P. Hajlasz, M. V. Korobkov, J. Kristensen. A bridge between Dubovitskii-Federer theorems and the coarea formula J. Funct. Anal. 272 (2017), 1265-1295. arXiv


[13] P. Hajlasz, X. Zhou, Sobolev homeomorphism on a sphere containing an arbitrary Cantor set in the image. Geom. Dedicata 184 (2016), 159-173. arXiv


[14] P. Hajlasz, S. Malekzadeh, A new characterization of the mappings of bounded length distortion. Int. Math. Res. Not. IMRN 2015, no. 24, 13238-13244. arXiv
[15] P. Hajlasz, S. Zimmerman, Geodesics in the Heisenberg group. Anal. Geom. Metr. Spaces 3 (2015), 325-337. arXiv
[16] P. Hajlasz, S. Malekzadeh, On conditions for unrectifiability of a metric space. Anal. Geom. Metr. Spaces 3 (2015), 1-14. arXiv


[17] Z. M. Balogh, P. Hajlasz, K. Wildrick, Weak contact equations for mappings into Heisenberg groups. Indiana Univ. Math. J. 63 (2014), 1839-1873. arXiv
[18] P. Hajlasz, Z. Liu, Maximal potentials, maximal singular integrals and the spherical maximal function. Proc. Amer. Math. Soc. 142 (2014), 3965-3974. arXiv
[19] P. Hajlasz, A. Schikorra, Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces. Ann. Acad. Sci. Fenn. Math. 39 (2014), 593-604. arXiv
[20] N. DeJarnette, P. Hajlasz, A. Lukyanenko, J. Tyson, On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target. Conform. Geom. Dyn. 18 (2014), 119-156. arXiv
[21] P. Hajlasz, A. Schikorra, J. Tyson, Homotopy groups of spheres and Lipschitz homotopy groups of Heisenberg groups Geom. Funct. Anal. 24 (2014), 245-268 arXiv


[22] P. Hajlasz, Z. Liu, Sobolev spaces, Lebesgue points and maximal functions J. Fixed Point Theory Appl. 13 (2013), 259-269. arXiv
[23] P. Hajlasz, J. Mirra, The Lusin theorem and horizontal graphs in the Heisenberg group Anal. Geom. Metr. Spaces 1 (2013), 295-301. pdf
[24] J. Gong, P. Hajlasz, Differentiability of p-harmonic functions on metric measure spaces. Potential Analysis 38 (2013), 79-93. pdf


[25] P. Goldstein, P. Hajlasz, Sobolev mappings, degree, homotopy classes and rational homology spheres. J. Geom. Anal. 22 (2012), 320-338. pdf


[26] P. Hajlasz, Sobolev mappings: Lipschitz density is not an isometric invariant of the target. Int. Math. Res. Not. IMRN Vol. 2011, no.12, 2794-2809. pdf


[27] P. Hajlasz, Z. Liu, A compact emebdding of a Sobolev space is equivalent to an emebdding into a better space. Proc. Amer. Math. Soc. 138 (2010), 3257-3266. pdf
[28] P. Hajlasz, J. Maly, On approximate differentiability of the maximal function. Proc. Amer. Math. Society. 138 (2010), 165--174.


[29] P. Hajlasz, Density of Lipschitz mappings in the class of Sobolev mappings between metric spaces. Math. Ann. 343 (2009), 801-823. pdf
[30] P. Hajlasz, Sobolev mappings between manifolds and metric spaces. In: Sobolev Spaces in Mathematics I. Sobolev type Inequalities pp. 185-222. International Mathematical Series. Springer 2009.


[31] P. Hajlasz, J. Tyson, Sobolev Peano cubes. Michigan Math. J. 56 (2008), 687-702.pdf
[32] P. Hajlasz, P. Strzelecki, X. Zhong, A new approach to interior regularity of elliptic systems with quadratic Jacobain structure in dimention two. Manuscripta Math. 127 (2008), 121-135.
[33] P. Hajlasz, P. Koskela, H. Tuominen, Measure density and extendability of Sobolev functions Rev. Mat. Iberoamericana 24 (2008), 645-669.
[34] P. Hajlasz, P. Koskela, H. Tuominen, Sobolev embeddings, extensions and measure density condition J. Funct. Anal. 254 (2008), 1217--1234.
[35] P. Hajlasz, T. Iwaniec, J. Maly, J. Onninen, Weakly differentiable mappings between manifolds. Memoirs Amer. Math. Soc. 899 (2008), 1--72.


[36] P. Hajlasz, Sobolev mappings: Lipschitz density is not a bi-Lipschitz invariant of the target. Geom. Funct. Anal. 17 (2007), 435-467. pdf


[37] B. Bojarski, P. Hajlasz, P. Strzelecki, Sard's theorem for mappings in Holder and Sobolev spaces. Manuscripta Math. 118 (2005), 383-397 pdf
[38] P. Hajlasz, P. Strzelecki, How to measure volume with a thread. Amer. Math. Monthly 112 (2005), 176-179.
pdf Read also Erratum


[39] P. Hajlasz, P. Koskela, Formation of cracks under deformations with finite energy. Calc. Var. Partial Differential Equations 19 (2004), 221--227.pdf
[40] P. Hajlasz, J. Onninen, On boundedness of maximal functions in Sobolev spaces. Ann. Acad. Sci. Fenn. Math. 29 (2004), no. 1, 167--176.


[41] P. Hajlasz, Whitney's example by way of Assouad's embedding. Proc. Amer. Math. Soc. 131 (2003), 3463--3467 pdf
[42] P. Hajlasz, A new characterization of the Sobolev space. (Dedicated to Professor Aleksander Pelczynski on the occasion of his 70th birthday.) Studia Math. 159 (2003), 263--275.
[43] P. Hajlasz, Sobolev spaces on metric-measure spaces. (Heat kernels and analysis on manifolds, graphs, and metric spaces (Paris, 2002)), 173--218, Contemp. Math. , 338, Amer. Math. Soc., Providence, RI, 2003.


[44] P. Hajlasz, J. Maly, Approximation in Sobolev spaces of nonlinear expressions involving the gradient Ark. Mat. 40 (2002), 245--274.pdf
[45] B. Bojarski, P. Hajlasz, P. Strzelecki, Improved $C^{k,\lambda}$ approximation of higher order Sobolev functions in norm and capacity. Indiana Univ. Mat. J. 51 (2002), 507--540.


[46] P. Hajlasz, Sobolev inequalities, truncation method, and John domains. (Papers on Analysis: A volume dedicated to Olli Martio on the occasion of his 60th birthday.) Report. Univ. Jyvaskyla 83 (2001), 109--126.pdf


[47] P. Hajlasz, P. Koskela, Sobolev met Poincare, Memoirs Amer. Math. Soc. 688 (2000), 1--101. pdf
[48] B. Franchi, P. Hajlasz, How to get rid of one of the weights in a two weight Poincare inequality?, Ann. Polon. Math 74 (2000), 97--103.
[49] P. Hajlasz, Sobolev mappings, co-area fromula and related topics. In: Proceedings on Analysis and Geometry. Novosibirsk: Sobolev Instinute Press, 2000, pp. 227--254.


[50] P. Hajlasz, Pointwise Hardy inequalities Proc. Amer. Math. Soc. 127(1999), 417--423. pdf
[51] B. Franchi, P. Hajlasz, P. Koskela, Definitions of Sobolev classes on metric spaces, Ann. Inst. Fourier (Grenoble) 49 (1999), 1903--1924.


[52] P. Hajlasz, P. Strzelecki, Subelliptic p-harmonic maps into spheres and the ghost of Hardy spaces, Math. Ann. 312 (1998), 341--362. pdf
[53] P. Hajlasz, P. Koskela, Isoperimetric inequalities and imbedding theorems in irregular domains, J. London Math. Soc. 58 (1998), 425-450.
[54] P. Hajlasz, J. Kinnunen, Holder quasicontinuity of Sobolev functions on metric spaces Rev. Mat. Iberoamericana, 14 (1998), 601--622.


[55] P.Hajlasz, O. Martio, Traces of Sobolev functions on fractal type sets and characterization of extension domains J. Funct. Anal., 143(1997), 221--246. pdf


[56] P. Hajlasz, Sobolev spaces on an arbitrary metric space, Potential Analysis , 5 (1996), 403--415. pdf
[57] P. Hajlasz, A counterexample to the $L^p$--Hodge decomposition, Banach Center Publications 33 (1996), 79--83.
[58] P. Hajlasz, On approximate differentiability of functions with bounded deformation Manuscripta Math. 91 (1996), 61--72.


[59] P. Hajlasz, P. Koskela, Sobolev meets Poincare, C. R. Acad Sci. Paris 320 (1995), 1211--1215. pdf
[60] P. Hajlasz, Boundary behaviour of Sobolev mappings, Proc. Amer. Math. Soc. , 123 (1995), 1145--1148.
[61] P. Hajlasz, A note on weak approximation of minors, Ann. I. H. P. Analyse non lineaire, 12 (1995), 415--424.
[62] P. Hajlasz, Geometric approach to Sobolev spaces and badly degenerate elliptic equations, GAKUTO International Series; Mathematical Sciences and Applications, vol. 7, (1995) pp. 141--168. Nonlinear Analysis and Applications (The Proceedings of Banach Center Minisemester, November-Decembed, 1994) N.Kenmochi, M. Niezgodka, P. Strzelecki eds.
[63] P. Hajlasz, A. Kalamajska, Polynomial asymptotics and approximation of Sobolev functions, Studia Math. 113(1995), 55--64.


[64] P. Hajlasz, Equivalent statement of the Poincare conjecture, Annali. Mat. Pura Appl. 167 (1994), 25--31. pdf
[65] P. Hajlasz, Approximation of Sobolev mappings, Nonlinear Analysis 22 (1994), 1579-1591.
[66] P. Hajlasz, A Sard type theorem for Borel mappings, Colloq. Math. 67 (1994), 217--221.


[67] B. Bojarski, P. Hajlasz, Pointwise inequalities for Sobolev functions and some applications. Studia Math. 106 (1993), 77--92.pdf
[68] P. Hajlasz, Change of variables formula under minimal assumptions. Colloq. Math. 64 (1993), 93--101.
[69] P. Hajlasz, Note on Meyers--Serrin's Theorem. Expositiones Math. 11 (1993), 377--379.
[70] P. Hajlasz, P. Strzelecki, On the differentiability of solutions of quasilinear elliptic equations, Colloq. Math. 64 (1993), 287--291.