Publications of Piotr Haj³asz

2012 and later

[1] P. Haj³asz, Z. Liu, Sobolev spaces, Lebesgue points and maximal functions (Preprint.)
[2] P. Haj³asz, Z. Liu, Maximal potentials, maximal singular integrals and the spherical maximal function (Preprint.) pdf
[3] J. Gong, P. Haj³asz, P. Koskela, X. Zhong, Imbeddings and higher-order Sobolev extensions. (Preprint.)
[4] P. Haj³asz, J. Tyson, Holder and Lipschitz Peano cubes and highly regular surjections between Carnot groups. (Prprint.)
[5] N. DeJarnette, P. Haj³asz, A. Lukyanenko, J. Tyson, On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target. (Preprint.) pdf
[6] P. Goldstein, P. Haj³asz, Sobolev mappings, degree, homotopy classes and rational homology spheres. J. Geom. Anal. 22 (2012), 320-338. pdf

2011

[7] J. Gong, P. Haj³asz, Differentiability of p-harmonic functions on metric measure spaces. Potential Analysis Published online December 2011. pdf
[8] P. Haj³asz, Sobolev mappings: Lipschitz density is not an isometric invariant of the target. Int. Math. Res. Not. IMRN Vol. 2011, no.12, 2794-2809. pdf

2010

[9] P. Haj³asz, 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
[10] P. Haj³asz, J. Maly, On approximate differentiability of the maximal function. Proc. Amer. Math. Society. 138 (2010), 165--174.
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2009

[11] P. Haj³asz, Density of Lipschitz mappings in the class of Sobolev mappings between metric spaces. Math. Ann. 343 (2009), 801-823. pdf
[12] P. Haj³asz, Sobolev mappings between manifolds and metric spaces. In: Sobolev Spaces in Mathematics I. Sobolev type Inequalities pp. 185-222. International Mathematical Series. Springer 2009.
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2008

[13] P. Haj³asz, J. Tyson, Sobolev Peano cubes. Michigan Math. J. 56 (2008), 687-702.pdf
[14] P. Haj³asz, 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.
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[15] P. Haj³asz, P. Koskela, H. Tuominen, Measure density and extendability of Sobolev functions Rev. Mat. Iberoamericana 24 (2008), 645-669.
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[16] P. Haj³asz, P. Koskela, H. Tuominen, Sobolev embeddings, extensions and measure density condition J. Funct. Anal. 254 (2008), 1217--1234.
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[17] P. Haj³asz, T. Iwaniec, J. Maly, J. Onninen, Weakly differentiable mappings between manifolds. Memoirs Amer. Math. Soc. 899 (2008), 1--72.
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2007

[18] P. Haj³asz, Sobolev mappings: Lipschitz density is not a bi-Lipschitz invariant of the target. Geom. Funct. Anal. 17 (2007), 435-467. pdf

2005

[19] B. Bojarski, P. Haj³asz, P. Strzelecki, Sard's theorem for mappings in Hölder and Sobolev spaces. Manuscripta Math. 118 (2005), 383-397 pdf
[20] P. Haj³asz, P. Strzelecki, How to measure volume with a thread. Amer. Math. Monthly 112 (2005), 176-179.
pdf Read also Erratum

2004

[21] P. Haj³asz, P. Koskela, Formation of cracks under deformations with finite energy. Calc. Var. Partial Differential Equations 19 (2004), 221--227.pdf
[22] P. Haj³asz, J. Onninen, On boundedness of maximal functions in Sobolev spaces. Ann. Acad. Sci. Fenn. Math. 29 (2004), no. 1, 167--176.
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2003

[23] P. Haj³asz, Whitney's example by way of Assouad's embedding. Proc. Amer. Math. Soc. 131 (2003), 3463--3467 pdf
[24] P. Haj³asz, A new characterization of the Sobolev space. (Dedicated to Professor Aleksander Pe³czyñski on the occasion of his 70th birthday.) Studia Math. 159 (2003), 263--275.
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[25] P. Haj³asz, 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.
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2002

[26] P. Haj³asz, J. Maly, Approximation in Sobolev spaces of nonlinear expressions involving the gradient Ark. Mat. 40 (2002), 245--274.pdf
[27] B. Bojarski, P. Haj³asz, P. Strzelecki, Improved $C^{k,\lambda}$ approximation of higher order Sobolev functions in norm and capacity. Indiana Univ. Mat. J. 51 (2002), 507--540.
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2001

[28] P. Haj³asz, 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. Jyväskylä 83 (2001), 109--126.pdf

2000

[29] P. Haj³asz, P. Koskela, Sobolev met Poincaré, Memoirs Amer. Math. Soc. 688 (2000), 1--101. pdf
[30] B. Franchi, P. Haj³asz, How to get rid of one of the weights in a two weight Poincaré inequality?, Ann. Polon. Math 74 (2000), 97--103.
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[31] P. Haj³asz, Sobolev mappings, co-area fromula and related topics. In: Proceedings on Analysis and Geometry. Novosibirsk: Sobolev Instinute Press, 2000, pp. 227--254.
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1999

[32] P. Haj³asz, Pointwise Hardy inequalities Proc. Amer. Math. Soc. 127(1999), 417--423. pdf
[33] B. Franchi, P. Haj³asz, P. Koskela, Definitions of Sobolev classes on metric spaces, Ann. Inst. Fourier (Grenoble) 49 (1999), 1903--1924.
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1998

[34] P. Haj³asz, P. Strzelecki, Subelliptic p-harmonic maps into spheres and the ghost of Hardy spaces, Math. Ann. 312 (1998), 341--362. pdf
[35] P.Haj³asz, P.Koskela, Isoperimetric inequalities and imbedding theorems in irregular domains, J. London Math. Soc. 58 (1998), 425-450.
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[36] P.Haj³asz, J.Kinnunen, Hölder quasicontinuity of Sobolev functions on metric spaces Rev. Mat. Iberoamericana, 14 (1998), 601--622.
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1997

[37] P.Haj³asz, O.Martio, Traces of Sobolev functions on fractal type sets and characterization of extension domains J. Funct. Anal., 143(1997), 221--246. pdf

1996

[38] P.Haj³asz, Sobolev spaces on an arbitrary metric space, Potential Analysis , 5 (1996), 403--415. pdf
[39] P.Haj³asz, A counterexample to the $L^p$--Hodge decomposition, Banach Center Publications 33 (1996), 79--83.
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[40] P.Haj³asz, On approximate differentiability of functions with bounded deformation Manuscripta Math. 91 (1996), 61--72.
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1995

[41] P.Haj³asz, P.Koskela, Sobolev meets Poincaré, C. R. Acad Sci. Paris 320 (1995), 1211--1215. pdf
[42] P.Haj³asz, Boundary behaviour of Sobolev mappings, Proc. Amer. Math. Soc. , 123 (1995), 1145--1148.
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[43] P.Haj³asz, A note on weak approximation of minors, Ann. I. H. P. Analyse non lineaire, 12 (1995), 415--424.
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[44] P.Haj³asz, 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. Niezgódka, P. Strzelecki eds.
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[45] P.Haj³asz, A.Ka³amajska, Polynomial asymptotics and approximation of Sobolev functions, Studia Math. 113(1995), 55--64.
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1994

[46] P.Haj³asz, Equivalent statement of the Poincaré conjecture, Annali. Mat. Pura Appl. 167 (1994), 25--31. pdf
[47] P.Haj³asz, Approximation of Sobolev mappings, Nonlinear Analysis 22 (1994), 1579-1591.
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[48] P.Haj³asz, A Sard type theorem for Borel mappings, Colloq. Math. 67 (1994), 217--221.
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1993

[49] B.Bojarski, P.Haj³asz, Pointwise inequalities for Sobolev functions and some applications. Studia Math. 106 (1993), 77--92.pdf
[50] P.Haj³asz, Change of variables formula under minimal assumptions. Colloq. Math. 64 (1993), 93--101.
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[51] P.Haj³asz, Note on Meyers--Serrin's Theorem. Expositiones Math. 11 (1993), 377--379.
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[52] P.Haj³asz, P.Strzelecki, On the differentiability of solutions of quasilinear elliptic equations, Colloq. Math. 64 (1993), 287--291.
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