Kontakt:

TF ČZU, M217/3

gurka@tf.czu.cz

Rozvrh, konzultace

Telefon:
(+420) 22438 3241

Důležité:

Katedra matematiky

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Jak studovat

Ke stažení:

Firefox

Počet přístupů:

177140

O mně

doc. RNDr. Petr Gurka, CSc.

Dosažené tituly a vzdělání

1996: doc. [habilitace v oboru Matematická analýza, Matematicko-fyzikální fakulta UK, Praha]

1987: CSc. [vědecká aspirantura v oboru Matematická analýza, Matematický ústav akademie věd ČR (MÚ AV ČR), Praha]

1986: RNDr. [rigorózní zkouška v oboru Matematická analýza, Matematicko-fyzikální fakulta UK, Praha]

1983: ekvivalent Mgr. [Matematicko-fyzikální fakulta UK, Praha, 1978–1983]

Odborné zaměření

Matematická analýza: teorie prostorů funkcí, funkcionální analýza, operátorová teorie, váhové nerovnosti, Fourierova analýza, teorie interpolací.

Profesionální kariéra

2016 (leden–květen): výuka, vědecká spolupráce (Ohio State University, Columbus, Ohio, USA)

Od roku 2012: docent (částečný úvazek na katedře matematiky VŠPJ v Jihlavě)

Od roku 1996: docent (na katedře matematiky České zemědělské univerzity v Praze)

1987–1996: odborný asistent (na katedře matematiky České zemědělské univerzity v Praze)

1992–1993: studijní pobyt (University of Sussex, Brighton, Anglie)

1983–1987: interní vědecká aspirantura (MÚ AV ČR, Praha)

Účast na mezinárodních vědeckých konferencích a studijních pobytech: Bulharsko, Polsko, USA, Velká Británie, Švédsko, SRN, Finsko, Španělsko.

Aktivní působení v tuzemských společnostech a organizacích: Jednota českých matematiků a fyziků (člen), Česká matematická společnost (člen)

Aktivní působení v zahraničních společnostech a organizacích: American Mathematical Society, USA (člen); Mathematical Reviews, USA (recenzent); Zentralblatt für Mathematik, SRN (recenzent); Journal of Mathematical inequalities, Chorvatsko (člen redakční rady)

Seznam publikací

Původní vědecké články

  1. P. Gurka, Generalized Hardy's inequality, Časopis Pěst. Mat. 109 (1984), no. 2, 194–204, MR 85m:26019.
  2. P. Gurka, B. Opic, Ar-condition for two weight functions and compact imbeddings of weighted Sobolev spaces, Czechoslovak Math. J. 38 (113) (1989), 611–617, MR 90a:46079.
  3. P. Gurka, B. Opic, Continuous and compact imbeddings of weighted Sobolev spaces I, Czechoslovak Math. J. 38 (113) (1988), 730–744, MR 89j:46034.
  4. P. Gurka, B. Opic, Continuous and compact imbeddings of weighted Sobolev spaces II, Czechoslovak Math. J. 39 (114) (1989), 78c94, MR 90e:46027.
  5. P. Gurka, B. Opic, Continuous and compact imbeddings of weighted Sobolev spaces III, Czechoslovak Math. J. 41 (1991), 317–341, MR 93a:46056.
  6. P. Gurka, L. Pick, A-type conditions for general measures in R1, Real Analysis Exchange 17 (1991/92), no. 2, 706–727, MR 93h:26024.
  7. P. Gurka, L. Pick, Errata to "A-type conditions for general measures in R1", Real Analysis Exchange 17 (1993/94), no. 1, 56–57, MR 95c:26017.
  8. B. Opic, P. Gurka, Weighted inequalities for geometric means, Proc. Amer. Math. Soc. 120 (1994), no. 3, 771–779, MR 94e:26036.
  9. D.E. Edmunds, P. Gurka, L. Pick, Compactness of Hardy-type integral operators in weighted Banach function spaces, Studia Math. 109 (1994), no. 1, 73–90.
  10. D.E. Edmunds, P. Gurka, B. Opic, Double exponential integrability of convolution operators in generalized Lorentz-Zygmund spaces, Indiana Univ. Math. J. 44 (1995), no. 1, 19–43.
  11. D.E. Edmunds, P. Gurka, B. Opic, Double exponential integrability, Bessel potentials and embedding theorems, Studia Math. 115 (1995), no. 2, 151–181.
  12. D.E. Edmunds, P. Gurka, B. Opic, Sharpness of embeddings in logarithmic Bessel potential spaces, Proc. Royal Soc. Edinburgh 126A (1996), 995–1009.
  13. A. Cianchi, D.E. Edmunds, P. Gurka, On weighted Poincare inequality, Math. Nachr. 180 (1996), 15–41.
  14. D.E. Edmunds, P. Gurka, B. Opic, On embeddings of logarithmic Bessel potential spaces, J. Functional Anal. 146 (1997), no. 1, 116–150.
  15. D.E. Edmunds, P. Gurka, B. Opic, Norms of embeddings of logarithmic Bessel potential spaces, Proc. Amer. Math. Soc. 126 (1998), no. 8, 2417–2425.
  16. P. Gurka, B. Opic, Global limiting embeddings of logarithmic Bessel potential spaces, Math. Inequal. Appl. 1 (1998), no. 4, 565–584.
  17. D.E. Edmunds, P. Gurka, B. Opic, Optimality of embeddings of logarithmic Bessel potential spaces, Quart. J. Math. Oxford Ser. 51 (2000), 185–209.
  18. P. Gurka, L. Pick, F.J. Martin-Reyes, P. Ortega, M.D. Sarrion, A. de la Torre, Good and bad measures, J. London Math. Soc. 61 (2000), 123–138.
  19. D.E. Edmunds, P. Gurka, B. Opic, Compact and continuous embeddings of logarithmic Bessel potential spaces, Studia Math. 168 (2005), no. 3, 229–250, MR2146125 (2006b:46040).
  20. P. Gurka, B. Opic, Sharp embeddings of Besov spaces with logarithmic smoothness, Rev. Mat. Complut. 18 (2005), no. 1, 81–110, MR2135533 (2006a:46039).
  21. D.E. Edmunds, P. Gurka, B. Opic, Non-compact and sharp embeddings of logarithmic Bessel potential spaces into Hölder-type spaces, Z. Anal. Anwend. 25 (2006), no. 1, 73–80, MR2216882 (2006k:46048).
  22. P. Gurka, B. Opic, Sharp embeddings of Besov-type spaces, J. Comput. Appl. Math. 208 (2007), no. 1, 235–269, MR2347748 (2008k:46097).
  23. P. Gurka, P. Harjulehto, A. Nekvinda, Bessel potential spaces with variable exponent, Math. Inequal. Appl. 10 (2007), no. 3, 661–676, MR2339558 (2008e:46038).
  24. P. Gurka, B. Opic, Hardy inequality of fractional order, Banach J. Math. Anal. 2 (2008), no. 2, 9–15. MR2391243
  25. D.E. Edmunds, P. Gurka, Entropy numbers of limiting embeddings of logarithmic Sobolev spaces into exponential spaces, Z. Anal. Anwend. 29 (2010), no. 2, 235–250.
  26. R. Černý, P. Gurka, S. Hencl, Concentration-Compactness Principle for generalized Trudinger inequalities, Z. Anal. Anwend. 30 (2011), no. 3, 355–375.
  27. R. Černý, P. Gurka, S. Hencl, On the Dirichlet problem for the n, ⍺-Laplacian with the nonlinearity in the critical growth range, Nonlinear Anal. 74 (2011), no. 15, 5189–5204.
  28. P. Gurka, J. Lang, Double-exponential embeddings of logarithmic spaces, Math. Nachr. 285 (2012), no. 2--3, 245--251.
  29. P. Gurka, B. Opic, Sharp Hardy inequalities of fractional order involving slowly varying functions, J. Math. Anal. Appl. 386 (2012), 728–737.
  30. D.E. Edmunds, P. Gurka, J. Lang, Properties of generalized trigonometric functions, J. Approx. Theory 164 (2012), 47–56.
  31. R. Černý, P. Gurka, Moser-type inequalities for generalized Lorentz-Sobolev spaces, Houston J. Math. 40 (2014), no. 4, 1225–1269.
  32. D.E. Edmunds, P. Gurka, J. Lang, Basis properties of generalized trigonometric functions, J. Math. Anal. Appl. 420 (2014), 1680–1692.
  33. D.E. Edmunds, P. Gurka, J. Lang, Decay of (p,q)-Fourier coefficients, Proc. R. Soc. A 470 (2014), no. 2170, 1–9.
  34. D.E. Edmunds, P. Gurka, J. Lang, Nuclearity and non-nuclearity of some Sobolev embeddings on domains, J. Approx. Theory 211 (2016), 94–103.
  35. Ö. Baksi, P. Gurka, J. Lang, O. Méndez, Basis properties of Lindqvist-Peetre functions in Lr(0,1)n, Rev. Mat. Complut. (to appear).

Publikace recenzované (příspěvky do sborníků z konferencí, přehledné články)

  1. B. Opic, P. Gurka, On imbeddings of weighted Sobolev spaces, Constructive Theory of Functions, Proceedings of the International Conference on Constructive Theory of Functions, Varna, May 25–31, Varna, 1987, pp. 360–366, MR 90e:46026.
  2. P. Gurka, B. Opic, A note on N-dimensional Hardy's inequality, Constructive Theory of Functions, Proceedings of the International Conference on Constructive Theory of Functions, Varna, May 25–31, Varna, 1987, pp. 194–196.
  3. B. Opic, P. Gurka, N-dimensional Hardy inequality and imbedding theorems for weighted Sobolev spaces on unbounded domains, Function Spaces, Differential Operators and Nonlinear Analysis, Proceedings of the International Summer School on Function Spaces, Differential Operators and Nonlinear Analysis held in Sodankyla, Longman, 1989, pp. 108–124, MR 91h:46064.
  4. P. Gurka, A. Kufner, A note on a two-weighted Sobolev inequality, Approximation and Function Spaces, Banach Center Publications, vol. 22, PWN-Polish Scientific Publishers, Warszaw, 1989, pp. 169–172, MR 92b:46040.
  5. P. Gurka, B. Opic, Imbeddings of weighted Sobolev spaces and the multiplicative inequality, Function Spaces, Proceedings of the 2nd International Conference in Poznań, Poland, August 28–September 2, 1989, Teubner Verlag, Stutgart-Leipzig, 1991, pp. 162–168.
  6. P. Gurka, On embeddings of logarithmic Bessel potential and Sobolev type spaces, Function Spaces, Differential Operators and Nonlinear Analysis (V. Mustonen and J. Rákosník, eds.), Proceedings of the Conference held in Syöte (Northern Finland), June 10–16, 1999, Math. Inst. AS CR, Praha, 2000, pp. 87–98.
  7. P. Gurka, Sharp embeddings of Besov spaces with logarithmic smoothness (elementary approach), Function Spaces, Differential Operators and Nonlinear Analysis (P. Drábek and J. Rákosník, eds.), Proceedings of the Conference held in Milovy (Czech Republic), May 28–June 2, 2004, Math. Inst. AS CR, Praha, 2005, pp. 113–122.
  8. P. Gurka, Critical embeddings of Sobolev type and some applications, Logos Polytechnikos 3 (2012), no. 4, 6–18.
  9. P. Gurka, A note on p;q-trigonometric functions, Logos Polytechnikos 5 (2014), no. 4, 122–129.

Další práce (disertace, preprinty apod.)

  1. P. Gurka, Generalized Hardy's inequality, spaces W1,p(Ω;α,β), W01,p(Ω;α,β), thesis, Faculty of Mathematics and Physics of the Charles University, Prague, 1987. (Czech)
  2. P. Gurka, Imbedding theorems in weighted Sobolev spaces, Ph.D. thesis, Mathematical Institute of the Czechoslovak Academy of Sciences, Prague, 1987. (Czech)
  3. P. Gurka, Limiting cases of Sobolev imbedding theorem, Real Analysis Exchange 20 (1994/95), no. 1, 48–49, abstract of the conference talk.