LIST OF PUBLICATIONS of Zoltán Buczolich

Papers submitted for publication are here.

  1. Z. Buczolich, On universal functions and series, Acta Math. Hungar. {\bf 49} (1987), no.~3-4, 403--414; MR 88k:42011

  2. Z. Buczolich, For every continuous $f$ there is an absolutely continuous $g$ such that $[f=g]$ is not bilaterally strongly porous, Proc. Amer. Math. Soc. {\bf 100} (1987), no.~3, 485--488; MR 88i:26025

  3. Z. Buczolich, An existence theorem for higher Peano derivatives in ${\bf R}\sp m$, Real Anal. Exchange {\bf 13} (1987/88), no.~1, 245--252; MR 89c:26018

  4. Z. Buczolich, Nearly upper semicontinuous gauge functions in ${\bf R}\sp m$, Real Anal. Exchange {\bf 13} (1987/88), no.~2, 436--440; MR 89f:26013

  5. Z. Buczolich, Continuous functions with everywhere infinite variation with respect to sequences, Proc. Amer. Math. Soc. {\bf 103} (1988), no.~2, 497--502; MR 89j:26005

  6. Z. Buczolich, Sets of convexity of continuous functions, Acta Math. Hungar. {\bf 52} (1988), no.~3-4, 291--303; MR 90c:26036

  7. Z. Buczolich, Every set of positive measure has a porous subset with difference set containing an interval, Real Anal. Exchange {\bf 14} (1988/89), no.~2, 501--505; MR 90d:28002

  8. Z. Buczolich and G. J. Sz\'ekely, A characterization of the uniform distribution via maximum likelihood estimation of its location parameter, in {\it Extreme value theory (Oberwolfach, 1987)}, 125--131, Lecture Notes in Statist., 51, Springer, New Y rk, 1989; MR 90g:62023

  9. Z. Buczolich, Ramsey type theorems for real functions, Mathematika {\bf 36} (1989), no.~1, 131--141; MR 90h:26012

  10. Z. Buczolich, Functions with finite intersections with analytic functions, Proc. Roy. Soc. Edinburgh Sect. A {\bf 112} (1989), no.~3-4, 271--275; MR 90i:26031

  11. Z. Buczolich, Second Peano derivatives are not extendable, Real Anal. Exchange {\bf 14} (1988/89), no.~2, 423--428; MR 90j:26004 Preprint: dvi or ps

  12. Z. Buczolich, Functions with all singular sets of Hausdorff dimension bigger than one, Real Anal. Exchange {\bf 15} (1989/90), no.~1, 299--306; MR 91c:26015

  13. Z. Buczolich, Henstock integrable functions are Lebesgue integrable on a portion, Proc. Amer. Math. Soc. {\bf 111} (1991), no.~1, 127--129; MR 91d:26011

  14. Z. Buczolich and G. J. Sz\'ekely, When is a weighted average of ordered sample elements a maximum likelihood estimator of the location parameter?, Adv. in Appl. Math. {\bf 10} (1989), no.~4, 439--456; MR 91e:62029

  15. Z. Buczolich and K. Ostaszewski, The Hausdorff dimension of graphs of density continuous functions, Proc. Amer. Math. Soc. {\bf 112} (1991), no.~4, 1037--1043; MR 91j:28008

  16. Z. Buczolich, Convexity and symmetric derivates of measurable functions, Real Anal. Exchange {\bf 16} (1990/91), no.~1, 187--196; MR 92a:26007

  17. Z. Buczolich, Density points and bi-Lipschitz functions in ${\bf R}\sp m$, Proc. Amer. Math. Soc. {\bf 116} (1992), no.~1, 53--59; MR 92k:26027 Preprint: dvi or ps

  18. Z. Buczolich and M. Laczkovich, Concentrated Borel measures, Acta Math. Hungar. {\bf 57} (1991), no.~3-4, 349--362; MR 92k:28002

  19. Z. Buczolich, A general Riemann complete integral in the plane, Acta Math. Hungar. {\bf 57} (1991), no.~3-4, 315--323; MR 93a:26008

  20. Z. Buczolich, Cantor type sets of positive measure and Lipschitz mappings, Real Anal. Exchange {\bf 17} (1991/92), no.~2, 702--705; MR 93d:28004

  21. A. M. Bruckner and Z. Buczolich, Attractive properties via generalized derivatives of continuous functions, Czechoslovak Math. J. {\bf 42(117)} (1992), no.~2, 271--278; MR 93h:26004 Preprint: dvi or ps

  22. Z. Buczolich, A $v$-integrable function which is not Lebesgue integrable on any portion of the unit square, Acta Math. Hungar. {\bf 59} (1992), no.~3-4, 383--393; MR 93h:28016

  23. Z. Buczolich, The $n$-dimensional gradient has the $1$-dimensional Denjoy-Clarkson property, Real Anal. Exchange {\bf 18} (1992/93), no.~1, 221--224; MR 94b:26012

  24. Z. Buczolich, M. J. Evans and P. D. Humke, Approximate high order smoothness, Acta Math. Hungar. {\bf 61} (1993), no.~3-4, 369--388; MR 94e:26009

  25. Z. Buczolich, The $g$-integral is not rotation invariant, Real Anal. Exchange {\bf 18} (1992/93), no.~2, 437--447; MR 94e:26023

  26. Z. Buczolich, No $b$-concentrated measures with $b<1.01$, Real Anal. Exchange {\bf 19} (1993/94), no.~2, 612--615; MR 95g:28006

  27. Z. Buczolich and K. Ostaszewski, The Hausdorff dimension of graphs of density continuous functions. II, Proc. Amer. Math. Soc. {\bf 123} (1995), no.~6, 1821--1825; MR 95g:28012

  28. Z. Buczolich, Product sets in the plane, sets of the form $A+B$ on the real line and Hausdorff measures, Acta Math. Hungar. {\bf 65} (1994), no.~2, 107--113; MR 95g:28016

  29. Z. Buczolich, Level sets of functions $f(x,y)$ with nonvanishing gradient, J. Math. Anal. Appl. {\bf 185} (1994), no.~1, 27--35; MR 95h:58013

  30. Z. Buczolich, Approximate continuity points of derivatives of functions of several variables, Acta Math. Hungar. {\bf 67} (1995), no.~3, 229--235; MR 96b:26015

  31. Z. Buczolich, Characterization of upper semicontinuously integrable functions, J. Austral. Math. Soc. Ser. A {\bf 59} (1995), no.~2, 244--254; MR 96f:26008

  32. Z. Buczolich, Unions of products of independent sets, Mathematika {\bf 42} (1995), no.~1, 25--29; MR 96g:28007 Preprint: dvi or ps

  33. M. Balcerzak, Z. Buczolich and M. Laczkovich, Lipschitz differences and Lipschitz functions, Colloq. Math. {\bf 72} (1997), no.~2, 319--324; MR 97k:26002 Preprint: dvi or ps

  34. Z. Buczolich and C. E. Weil, Extending Peano differentiable functions, Atti Sem. Mat. Fis. Univ. Modena {\bf 44} (1996), no.~2, 323--330; MR 98b:26002

  35. Z. Buczolich, Another note on the gradient problem of C. E. Weil, Real Anal. Exchange {\bf 22} (1996/97), no.~2, 775--784; MR 98g:26012

  36. Z. Buczolich, Arithmetic averages of rotations of measurable functions, Ergodic Theory Dynam. Systems {\bf 16} (1996), no.~6, 1185--1196; MR 98g:28018

  37. Z. Buczolich and W. F. Pfeffer, Variations of additive functions, Czechoslovak Math. J. {\bf 47(122)} (1997), no.~3, 525--555; MR 98h:26017 Preprint: dvi or ps

  38. Z. Buczolich, U. B. Darji and R. J. O'Malley, Irrational rotations and differentiability, Acta Math. Hungar. {\bf 78} (1998), no.~4, 305--313; MR 99b:26005

  39. Z. Buczolich, Functions of two variables with large tangent plane sets, J. Math. Anal. Appl. {\bf 220} (1998), no.~2, 562--570; MR 99b:26017 Preprint: dvi or ps

  40. Z. Buczolich, Lipschitz images with fractal boundaries and their small surface wrapping, Proc. Amer. Math. Soc. {\bf 126} (1998), no.~12, 3589--3595; MR 99b:28007 Preprint: dvi or ps

  41. Z. Buczolich and W. F. Pfeffer, On absolute continuity, J. Math. Anal. Appl. {\bf 222} (1998), no.~1, 64--78; CNO CMP 1 623 859 Preprint: dvi or ps

  42. Z. Buczolich and W. F. Pfeffer, When absolutely continuous implies $\sigma$-finite, Acad. Roy. Belg. Bull. Cl. Sci. (6) {\bf 8} (1997), no.~1-6, 155--160; CNO CMP 1 625 113

  43. Z. Buczolich, BV-Sets, Functions and Integrals, Acta Univ. Carolinae, {\bf 39} (1998), (1-2), 99-104.

  44. Z. Buczolich, J-P. Kahane, R. D. Mauldin, Sur les s\'eries de translat\'ees de fonctions positives, C. R. Acad. Sci. Paris, t. 329, S\'erie I, p. 261-264, 1999. Preprint: dvi or ps

  45. Z. Buczolich, Ergodic averages and free {\bf Z}$_2$ actions, Fund. Math. 160 (1999) 247-254. Preprint: dvi or ps

  46. Z. Buczolich and C. E. Weil, The Non-coincidence of Ordinary and Peano Derivatives, Math. Boh. 124 (1999) No. 4, 381-399. Preprint: dvi or ps

  47. Z. Buczolich, T. De Pauw, and W. F. Pfeffer, Multipliers for generalized Riemann Integrals, C. R. Math. Acad. Sci. Soc. R. Can., Vol. 21 (4), (1999) 139-145. Preprint: dvi or ps

  48. Z. Buczolich, T. De Pauw-val and W. Pfeffer, Charges, BV Functions, and Multipliers for Generalized Riemann Integrals, Indiana Univ. Math. J. Vol. 48, No. 4 (1999), 1471-1511. Preprint: dvi or ps

  49. Z. Buczolich, Lipeomorphisms, sets of bounded variation and integrals, Acta Math. Hung., 87(3), (2000), 243-265. Preprint (new version since 10.10/99): dvi or ps

  50. K. M. Brucks and Z. Buczolich, Trajectory of the turning point is dense for a co-$sigma$-porous set of tent maps, Fund. Math. 165 (2000), 95-123. Preprint : dvi or ps

  51. K. M. Brucks and Z. Buczolich, Universality in inverse limit spaces of the logistic famliy occurs with positive measure, Atti. Sem. Univ. Modena, {\bf 48} (2000), no. 2, 335-353. Preprint: dvi or ps

  52. Z. Buczolich and A. Olevskii, Spectral boundary of complemented invariant subspaces in $L^{p}({\bf R})$, Proc. Roy. Soc. Edinburgh, Sect. A, {\bf 131} (2001), no. 4, 785-798. Preprint server of Max Planck Institute, Bonn.

  53. Z. Buczolich and D. Mauldin, On the convergence of $\sum_{n=1}^{\infty}f(nx)$ for measurable functions, Mathematika, {\bf 46} (1999), no. 2, 337-341. Preprint: dvi or ps

  54. Z. Buczolich and J. Nagy, H\"older spectrum of typical monotone continuous functions, Real Anal. Exchange, {\bf 26} (2000/01), no. 1, 133-156. Preprint: dvi or ps

  55. Z. Buczolich, J-P. Kahane and D. Mauldin, On series of translates of positive functions, Acta Math. Hungar., {\bf 93(3)} (2001), 171-188. Preprint: ps

  56. Z. Buczolich, Tensor products of AC* charges and AC Radon measures are not always AC* charges, J. Math. Anal. Appl. {\bf 259} (2001), no. 2, 377-385. Preprint: dvi or ps

  57. Z. Buczolich, When tensor products of AC* charges and Radon measures are AC* charges, Atti Sem. Mat. Fis. Univ. Modena., IL, (2001) 411-454. Preprint: ps

  58. Z. Buczolich and D. Mauldin, On series of translates of positive functions II., Indag. Mathem., N. S., {\bf 12} (3), (2001), 317-327. Preprint: ps

  59. Z. Buczolich, Micro Tangent Sets of Continuous Functions,  Math. Bohem.  128  (2003),  no. 2, 147--167.  Preprint: pdf or ps

  60. Z. Buczolich, Category of density points of fat Cantor sets,  Real Anal. Exchange 29 (2003/04), no. 1, 497--502.Preprint: pdf or ps

  61. Z. Buczolich and C. E. Weil, Infinite Peano Derivatives, extensions, and the Baire one property, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia 52 (2004), no. 1, 117--149 (2005): pdf or ps .

  62. I. Assani, Z. Buczolich and D. Mauldin, An L^1 Counting problem in Ergodic Theory, J. Anal. Math. 95 (2005), 221--241. Preprint : pdf or ps

  63. I. Assani, Z. Buczolich and D. Mauldin, Counting and convergence in Ergodic Theory, 32nd Winter School on Abstract Analysis. Acta Univ. Carolin. Math. Phys. 45 (2004), no. 2, 5--21.. Preprint: pdf or ps

  64. Z. Buczolich and U. B. Darji, Pseudoarcs, Pseudocircles, Lakes of Wada and Generic Maps on S^2, Topology Appl. 150 (2005), no. 1-3, 223--254.. Preprint: pdf  or ps

  65. Z. Buczolich, Solution to the gradient problem of C. E. Weil, Rev. Mat. Iberoamericana, 21 (2005) No. 3., 889-910. Preprint: pdf or ps

  66. Z. Buczolich and A. Máthé, Where are typical C^1 functions one-to-one?, Math. Bohem. 131 (2006), no. 3, 291--303. pdf or ps.

  67. Z. Buczolich and D. Mauldin, Concepts behind divergent ergodic averages along the squares, Ergodic Theory and Related Fields, American Mathematical Society, Contemporary Mathematics Vol. 430, (2007) 41-56. pdf.                    

  68. Z. Buczolich and Cs. Ráti, Micro Tangent sets of  typical continuous functions, Atti. Semin. Mat. Fis. Univ. Modena Reggio Emilia, 54 (2006), 135-136, Preprint: pdf.            

  69. Z. Buczolich, Universally $L^1$ good sequences with gaps tending to infinity, Acta Math. Hungar., 117 (1-2) (2007), 91-40, Preprint: pdf .
  70. Z. Buczolich, Irregular $1$-sets on the graphs of continuous functions, Acta Math. Hungar., 121 (4) (2008), 371-393. Preprint:pdf .
  71.  I. Assani and Z. Buczolich, A maximal inequality for the tail of the bilinear Hardy-Littlewood function,   Ergodic theory, 7--11, Contemp. Math., 485, Amer. Math. Soc., Providence, RI, 2009, Preprint: pdf .
  72. Z. Buczolich, Almost everywhere convergence of ergodic averages,   Real Anal. Exchange 34 (2009), no. 1, 1--15, Preprint: pdf.
  73. I. Assani and Z. Buczolich,  The $(L^{1},L^{1})$ bilinear Hardy-Littlewood function and F\"urstenberg averages,  Rev. Mat. Iberoamericana Volume 26, Number 3 (2010), 861-890, Preprint: pdf

  74. Z. Buczolich and D. Mauldin, Divergent Square Averages, Ann. of Math. (2) 171 (2010),  pp. 1479-1530 Preprint:  pdf.   

  75. I. Assani and Z. Buczolich,  The (Lp, Lq) bilinear Hardy-Littlewood function for the tail.
    ISRAEL JOURNAL OF MATHEMATICS 179:(1) pp. 173-187. (2010), Preprint: pdf.   

  76. Buczolich Zoltán, Seuret Stéphane
    Typical Borel measures on [0, 1]d satisfy a multifractal formalism.
    NONLINEARITY 23:(11) pp. 2905-2911. (2010), Dokumentum a kiadónál
    Preprint: pdf.   

  77. Z. Buczolich, Non-$L^{1}$ functions with rotation sets of Hausdorff dimension one, ACTA MATHEMATICA HUNGARICA 126:(1-2) pp. 23-50. (2010)
      DOI 10.1007/s10474-009-8204-0, 2009, to appear, Preprint: pdf.      Official link:

  78. Z. Buczolich, Occupation measure and level sets of the Weierstrass-Cellerier function. Recent developments in fractals and related fields, 3–18, Appl. Numer. Harmon. Anal., Birkhäuser Boston, Inc., Boston, MA, 2010. Preprint: pdf.

  79. Z. Buczolich and S. Seuret, Singularity spectrum of generic $\alpha$-H\"older regular functions after time subordination, Journal of Fourier Analysis and Applications, 2011, Volume 17, Number 3, Pages 457-485. Preprint: pdf

  80. Buczolich, Zoltán; Seuret, Stéphane Multifractal spectrum and generic properties of functions monotone in several variables. J. Math. Anal. Appl. 382 (2011), no. 1, 110–126. Preprint: pdf

  81. Balka, Richárd; Buczolich, Zoltán; Elekes, Márton Topological Hausdorff dimension and level sets of generic continuous functions on fractals. Chaos Solitons Fractals 45 (2012), no. 12, 1579–1589. Preprint: pdf arXiv

  82. Brémont, Julien; Buczolich, Zoltán Maximizing points and coboundaries for an irrational rotation on a circle. Ergodic Theory Dynam. Systems 33 (2013), no. 1, 24–48. Preprint: pdf

  83.  Z. Buczolich, Averages along the squares on the torus. Ergodic theory and dynamical systems, 67–79, De Gruyter Proc. Math., De Gruyter, Berlin, 2014. Preprint: pdf.           

  84. R. Balka, Z. Buczolich and M. Elekes, A new fractal dimension: The topological Hausdorff dimension. Adv. Math. 274 (2015), 881–927. Preprint: pdf, arXiv

  85. Z. Buczolich and S. Seuret, Measures and functions with prescribed homogeneous multifractal spectrum, J. Fractal Geom. 1 (2014), no. 3, 295–333.
    Preprint: pdf.


  1. Restriction and Intersection Theorems in Real Analysis, Real Anal. Exchange, Vol. 15 No. 1, 1989-90, 26-29. (This is an English abstract of my Ph. D. Thesis.) Preprint: dvi or ps

  2. Generalized integrals and related topics, Real Anal. Exchange, Vol. 23 No. 1, 1997-98, 27-36. (This is an English Abstract of my Habilitation Thesis.) Preprint: dvi or ps

  3. $\sum f(nx)$ konvergenciájáról, (In Hungarian. Talk given at the Hungarian Academy of Sciences on the occasion of the 75th birthday of Á. Császár.) Preprint: dvi or ps

  4. On the gradient problem of C. E. Weil, to appear in conference reports of the Real Anal. Exchange. Preprint: pdf or ps