Publications of Antti Vähäkangas


    A book

  1. Kinnunen, J., J. Lehrbäck and A. Vähäkangas, Maximal Function Methods for Sobolev Spaces, Mathematical Surveys and Monographs, Volume 257, American Mathematical Society. [AMS-bookstore]

    2. Articles submitted for publication

  2. Ihnatsyeva, L., K. Mohanta and A.V. Vähäkangas, Fractional Hardy inequalities and capacity density. [arXiv]
    3.  
  3. Lehrbäck, J., K. Mohanta and A.V. Vähäkangas, Classifying Triebel-Lizorkin capacities in metric spaces. [arXiv]


    4. Articles in international refereed journals

  4. Kline, J. and A.V. Vähäkangas, Characterization of the upper Assouad codimension. J. Math. Soc. Japan, accepted for publication. [arXiv]
    5.  
  5. Hurri-Syrjänen, R., J. C. Martínez-Perales, C. Pérez and A.V. Vähäkangas, On the weighted inequality between the Gagliardo and Sobolev seminorms, Israel J. Math., accepted for publication. [arXiv]
    6.  
  6. Anderson, T.C., J. Lehrbäck, C. Mudarra and A.V. Vähäkangas, Weakly porous sets and Muckenhoupt A_p distance functions, J. Funct. Anal., doi: 10.1016/j.jfa.2024.110558. [PDF]
    7.  
  7. Canto, J., L. Ihnatsyeva, J. Lehrbäck and A.V. Vähäkangas, Capacities and density conditions in metric spaces, Potential Anal., doi: 10.1007/s11118-024-10137-5. [PDF]
    8.  
  8. Hurri-Syrjänen, R., J. C. Martínez-Perales, C. Pérez and A.V. Vähäkangas, On the BBM-phenomenon in fractional Poincaré-Sobolev inequalities with weights, Int. Math. Res. Not., Volume 2023, Issue 20 (2023), 17205-17244, doi: 10.1093/imrn/rnac246. [PDF]
    9.  
  9. Canto, J. and A.V. Vähäkangas, The Hajłasz capacity density condition is self-improving, J. Geom. Anal., Volume 32, Number 11 (2022), doi: 10.1007/s12220-022-00979-z. [PDF]
    10.  
  10. Dyda, B., J. Lehrbäck, and A.V. Vähäkangas, Fractional Poincaré and localized Hardy inequalities on metric spaces, Adv. Calc. Var., Volume 16, Number 4 (2023), 867-884, doi: 10.1515/acv-2021-0069. [PDF]
    11.  
  11. Ihnatsyeva L., J. Lehrbäck and A.V. Vähäkangas, Hardy-Sobolev inequalities and weighted capacities in metric spaces, Math. Scand., Volume 128, Number 3 (2022), doi: 10.7146/math.scand.a-133257. [PDF]
    12.  
  12. Kurki, E-K. and A.V. Vähäkangas, Weighted norm inequalities in a bounded domain by the sparse domination method, Rev. Mat. Complut. 34 (2021), 435-467, doi: 10.1007/s13163-020-00358-8. [PDF]
    13.  
  13. Eriksson-Bique, S., J. Lehrbäck and A.V. Vähäkangas, Self-improvement of weighted pointwise inequalities on open sets, J. Funct. Anal, Volume 279, Issue 7 (2020), doi: 10.1016/j.jfa.2020.108691. [PDF]
    14.  
  14. Eriksson-Bique, S. and A.V. Vähäkangas, Self-improvement of pointwise Hardy inequality, Trans. Amer. Math. Soc. 372 (2019), 2235-2250, doi: 10.1090/tran/7826. [PDF]
    15.  
  15. Kinnunen, J., R. Korte, J. Lehrbäck and A.V. Vähäkangas, A maximal function approach to two-measure Poincaré inequalities, J. Geom. Anal., Volume 29 (2019), 1763-1810, doi: 10.1007/s12220-018-0061-z. [PDF]
    16.  
  16. Kinnunen, J., J. Lehrbäck, A.V. Vähäkangas and X. Zhong, Maximal function estimates and self-improvement results for Poincaré inequalities, Manuscripta Math., Volume 158, Issue 1-2 (2019), 119-147. [PDF]
    17.  
  17. Dyda, B., J. Lehrbäck, and A.V. Vähäkangas, Fractional Hardy-Sobolev type inequalities for half spaces and John domains, Proc. Amer. Math. Soc., Volume 146, Number 8 (2018), 3393-3402. [PDF]
    18.  
  18. Dyda, B., L. Ihnatsyeva, J. Lehrbäck, H. Tuominen and A.V. Vähäkangas, Muckenhoupt A_p-properties of distance functions and applications to Hardy-Sobolev -type inequalities, Potential Anal., Volume 50, Issue 1 (2019), 83-105. [PDF]
    19.  
  19. Luiro, H. and A.V. Vähäkangas, Beyond local maximal operators, Potential Anal., Volume 46, Issue 2 (2017), 201-226. [PDF]
    20.     
  20. Lehrbäck, J., H. Tuominen and A.V. Vähäkangas, Self-improvement of uniform fatness revisited, Math. Ann., Volume 368, Issue 3-4 (2017), 1439-1464. [PDF]
    21.     
  21. Lehrbäck, J. and A.V. Vähäkangas, In between the inequalities of Sobolev and Hardy, J. Funct. Anal, Volume 271, Issue 2 (2016), 330-364. [PDF]
    22.     
  22. Dyda, B., L. Ihnatsyeva and A.V. Vähäkangas, On improved fractional Sobolev-Poincaré inequalities, Ark. Mat., Volume 54, Issue 2 (2016), 437-454. [PDF]
    23.     
  23. Luiro, H. and A.V. Vähäkangas, Local maximal operators on fractional Sobolev spaces, J. Math. Soc. Japan, Volume 68, Number 3 (2016), 1357-1368. [PDF]
    24.     
  24. Hurri-Syrjänen, R., N. Marola and A.V. Vähäkangas, Poincaré inequalities in quasihyperbolic boundary condition domains, Manuscripta Math., Volume 148, Issue 1 (2015), 99-118. [PDF]
    25.     
  25. Ihnatsyeva, L., J. Lehrbäck, H. Tuominen and A.V. Vähäkangas, Fractional Hardy inequalities and visibility of the boundary, Studia Math., Volume 224, Number 1 (2014), 47-80. [PDF]
    26.     
  26. Hurri-Syrjänen, R. and A.V. Vähäkangas, Fractional Sobolev-Poincare and fractional Hardy inequalities in unbounded John domains, Mathematika, Volume 61, Issue 02 (2015), 385-401. [PDF]
    27.     
  27. Hurri-Syrjänen, R., N. Marola and A.V. Vähäkangas, Aspects of local-to-global results, Bull. London Math. Soc., Volume 46, Issue 5 (2014), 1032-1042. [PDF]
    28.     
  28. Dyda, B. and A.V. Vähäkangas, A framework for fractional Hardy inequalities, Ann. Acad. Sci. Fenn. Math., Volume 39 (2014), 675-689. [PDF]
    29.     
  29. Dyda, B. and A.V. Vähäkangas, Characterizations for fractional Hardy inequality, Adv. Calc. Var., Volume 8, Issue 2 (2015), 173-182. [PDF]
    30.     
  30. Lacey, M.T. and A.V. Vähäkangas, On the Local Tb Theorem: A Direct Proof under the Duality Assumption, Proc. Edinb. Math. Soc., Volume 59, Issue 1 (2016), 193-222. [PDF]
    31.     
  31. Ihnatsyeva, L. and A.V. Vähäkangas, Hardy inequalities in Triebel-Lizorkin spaces II. Aikawa dimension, Ann. Mat. Pura Appl. (4), Volume 194, Issue 2 (2015), 479-493. [PDF]
    32.     
  32. Hytönen, T.P. and A.V. Vähäkangas, The local non-homogeneous Tb theorem for vector-valued functions, Glasg. Math. J., Volume 57, Issue 1 (2015), 17-82. [PDF]
    33.     
  33. Ihnatsyeva, L. and A.V. Vähäkangas, Characterization of traces of smooth functions on Ahlfors regular sets, J. Funct. Anal., Volume 265, Issue 9 (2013), 1870-1915. [PDF]
    34.     
  34. Harjulehto, P., Hurri-Syrjänen, R. and A.V. Vähäkangas, On the (1,p)-Poincaré inequality, Illinois J. Math., volume 56, number 3 (2012), 905-930. [PDF]
    35.     
  35. Ihnatsyeva, L. and A.V. Vähäkangas, Hardy inequalities in Triebel-Lizorkin spaces, Indiana Univ. Math. J., Volume 62, Issue 6 (2013), 1785-1807. [PDF]
    36.     
  36. Lacey, M.T. and A.V. Vähäkangas, The Perfect Local Tb Theorem and Twisted Martingale Transforms, Proc. Amer. Math. Soc., volume 142, Number 5 (2014), 1689-1700. [PDF]
    37.     
  37. Edmunds, D.E., R. Hurri-Syrjänen and A.V. Vähäkangas, Fractional Hardy-type inequalities in domains with uniformly fat complement, Proc. Amer. Math. Soc., Volume 142, Number 3 (2014), 897-907. [PDF]
    38.     
  38. Hurri-Syrjänen, R. and A.V. Vähäkangas, On fractional Poincaré inequalities, J. Anal. Math., Volume 120, Issue 1 (2013), 85-104. [PDF]
    39.     
  39. Vähäkangas, A.V., On regularity and extension of Green's operator on bounded smooth domains, Potential Anal., Volume 37, Issue 1 (2012), 57-77. [PDF]
    40.     

    Articles in international refereed conference proceedings

  40. Hurri-Syrjänen, R. and A.V. Vähäkangas, Characterizations to the fractional Sobolev inequality, Complex Analysis and Dynamical Systems VII, 145-154, Contemp. Math., 699, Amer. Math. Soc., Providence, RI, 2017. [PDF]
    41.     
  41. Lacey, M.T. and A.V. Vähäkangas, Non-Homogeneous Local T1 Theorem: Dual Exponents, in Some Topics in Harmonic Analysis and Applications, ALM 34, International Press (2016), 231-264.


    42. A dissertation

  42. Vähäkangas, A.V., Boundedness of weakly singular integral operators on domains, Ann. Acad. Sci. Fenn. Math. Diss. No. 153, 2009. Doctoral Dissertation. [PDF]