scientific publications

1. Relações algébrico-topológicas no contexto da teoria dos operadores, Trabalho de síntese para as Provas de Aptidão Pedagógica e Capacidade Científica, Departamento de Matemática da Universidade de Coimbra, 1987.

2. Weyl numbers in function spaces, Forum Math. 2 (1990), 249-263.

3. Some domains where the eigenvalues of the Dirichlet Laplacian have non-power second term asymptotic estimates, J. London Math. Soc. (2) 43 (1991), 431-450.

4. Weyl numbers in function spaces II, Forum Math. 3 (1991), 613-621.

5. Asymptotic distribution of Weyl  numbers  and  eigenvalues, D.Phil. thesis, University of Sussex, 1991.

6. Weyl numbers in sequence spaces and sections of unit balls, J. Funct. Anal. 106 (1992), 1-17.

7. On the search for the asymptotic behaviour of the eigenvalues of the Dirichlet Laplacian for bounded irregular domains, International Journal of Applied Science & Computations 2 (1995), 261-287.

8. Eigenvalue asymptotics of the Stokes operator for fractal domains, Proc. London Math. Soc. (3) 76 (1998), 579-602 (there exists a more detailed version of this paper as preprint CM/I-10, Universidade de Aveiro, 1995).

9. Eigenvalue distribution for the Stokes operator, IKM 97: Digital Proceedings \Proc97\Docs\145\145ikm97, Bauhaus-Universität, Weimar, 1997.

10. About approximation numbers in function spaces, J. Approx. Theory 94 (1998), 383-395.

11. Entropy numbers of embeddings between logarithmic Sobolev spaces, Port. Math. 57 (3) (2000), 355-379.

12. Approximation by functions of compact support on irregular domains, Proceedings of Conference “Function Spaces, Differential Operators and Nonlinear Analysis”, Syöte, 1999, Math. Inst. Acad. Sci. Czech Republic, 2000, 35-40.

13. Approximation by functions of compact support in Besov-Triebel-Lizorkin spaces on irregular domains, Studia Math. 142 (1) (2000), 47-63.

14. On fractals which are not so terrible, Fund. Math. 171 (2002), 249-266.

15. (with Susana Moura) Local growth envelopes of spaces of generalized smoothness: the subcritical case, Math. Nachr. 273 (2004), 43-57.

16. (with Dorothee Haroske) Sharp estimates of approximation numbers via growth envelopes, Proceedings of Conference “Function Spaces, Differential Operators, Nonlinear Analysis – the Hans Triebel Anniversary Volume”, Teistungen, 2001, Birkhäuser, Basel, 2003, 237-244).

17. (with Susana Moura) Local growth envelopes of spaces of generalized smoothness: the critical case, Math. Ineq. & Appl. 7 (2004), 573-606.

18. Subatomic representation of Bessel potential spaces modelled on Lorentz spaces, Textos de Matemática, Série B, 34 - "The J. A. Sampaio Martins Anniversary Volume", Coimbra, 2004, 37-47.

19. Growth envelopes in Function Spaces, lecture of synthesis, Provas de Agregação emMatemática, Universidade de Aveiro, 2004.

20. (with Dorothee Haroske) Continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbers, J. Function Spaces Appl. 3 (2005), 33-71.

21. (with Andrey Sarychev and Dina Seabra) An example of the Lavrentiev phenomenon in 2D, Proceedings of the 3^rd Junior European Meeting on Control, Optimization and Computation (M. Guerra, D. Torres ed.), Aveiro, 2005, 113-124.

22. (with Andrey Sarychev and Dina Seabra) Two-dimensional stable Lavrentiev phenomenon with and without boundary conditions, Control & Cybernetics 34 (2005), 689-707.

23. (with Walter Farkas) Local growth envelopes of Besov spaces of generalised smoothness, Zeit. Anal. Anw. 25 (2006), 265-298 (see also preprint CM 04/I-24, Universidade de Aveiro, 2004).

24. (with H.-G. Leopold) Local growth envelopes of Triebel-Lizorkin spaces of generalized smoothness, J. Fourier Anal. Appl. 12 (2006), 427-445.

25. (with S. Lopes and H. Triebel) A homogeneity property for Besov spaces, J. Function Spaces Appl. 5 (2007), 123-132.

26. (with A. Gogatishvili and B. Opic) Sharp embeddings of Besov spaces involving only logarithmic smoothness, Journal Approx. Theory 152 (2008), 188-214.

27. (with S. Lopes) Homogeneity, non-smooth atoms and Besov spaces of generalised smoothness on quasi-metric spaces, Diss. Math., 460, 2009, 44 pp.

28. (with A. Almeida) Generalized Hardy spaces, Acta Mathematica Sinica (English Series), 26(9), 2010, 1673-1692.

29. (with S. Lopes) Spectral theory for the fractal Laplacian in the context of h-sets, Math. Nachr. 284(1), 2011, 5-38, DOI 10.1002/mana.200910214.

30. (with S. Lopes) The fractal Dirichlet Laplacian, Rev. Mat. Complut. 24 (2011), 189–209, DOI: 10.1007/s13163-010-0035-6.

31. (with A. Almeida) Real interpolation of generalized Besov-Hardy spaces and applications, J. Fourier Anal. Appl. 17(4), 2011, 691-719, DOI: 10.1007/s00041-010-9145-2.

32. (with A. Gogatishvili and B. Opic) Compact embeddings of Besov spaces involving only slowly varying smoothness, Czechoslovak Mathematical Journal, 61(136), 2011, 923-940, DOI: 10.1007/s10587-011-0060-8.

33. On the type of convergence in atomic representations, Complex Variables and Elliptic Equations, 56 (2011), 875-883.

34. (with A. Gogatishvili and B. Opic) Embeddings and the growth envelope of Besov spaces involving only slowly varying smoothness, J. Approx. Theory 163 (2011), 1373-1399, doi:10.1016/j.jat.2011.03.005 (see also a somewhat different version entitled Sharp embeddings of Besov spaces involving only slowly varying smoothness, Preprint 177, IM ASCR, Prague, 2008).

35. (with A. Carvalho) On the Hausdorff dimension of continuous functions belonging to Hölder and Besov spaces on fractal d-sets, J. Fourier Anal. Appl. 18 (2012), 386-409, DOI: 10.1007/s00041-011-9202-5.

36. Growth envelopes of Besov spaces on fractal h-sets, Math. Nachr. 286 (2013), 550-568, DOI: 10.1002/mana.201100176.

37. (with H.-G. Leopold) On generalized Besov and Triebel-Lizorkin spaces of regular distributions, J. Funct. Anal. 264 (2013), 2676-2703, http://dx.doi.org/10.1016/j.jfa.2013.03.012.

38. (with Dorothee Haroske) Traces for Besov spaces on fractal h-sets and dichotomy results, Studia Math. 231 (2015), 117-147, http://dx.doi.org/10.4064/sm8171-1-2016.

39. (with Dorothee Haroske) Embeddings of Besov spaces on fractal h-sets, Banach J. Math. Anal. 9(4), 2015, 259-295, http://dx.doi.org/10.15352/bjma/09-4-14.

40. (with A. Gogatishvili and B. Opic) Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces, Proceedings of the Royal Society of Edinburgh, Section A, Mathematics, 146 (2016), 905-927, http://dx.doi.org/10.1017/S0308210515000761.

41. (with Alexandre Almeida) On 2-microlocal spaces with all exponents variable, Nonlinear Analysis 135 (2016), 97-119, http://dx.doi.org/10.1016/j.na.2016.01.016.

42. (with Alexandre Almeida) Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applications, J. Funct. Anal. 270 (2016), 1888-1921, http://dx.doi.org/10.1016/j.jfa.2015.11.010.

43. (with Henning Kempka) Variable exponent Triebel-Lizorkin-Morrey spaces, J. Math. Anal. Appl. 484, 1 (2020) 123712, https://doi.org/10.1016/j.jmaa.2019.123712.

44. (with Alexandre Almeida) Variable exponent Besov-Morrey spaces, J. Fourier Anal. Appl. 26, 5 (2020) https://doi.org/10.1007/s00041-019-09711-y, https://rdcu.be/b0dWc.

45. (with Henning Kempka), Decompositions with atoms and molecules for variable exponent Triebel-Lizorkin-Morrey spaces, Constr. Approx. 53 (2021), 201–234, http://dx.doi.org/10.1007/s00365-020-09497-z, https://rdcu.be/b0Bl7.

46. (with D. P. Hewett and A. Moiola) Density results for Sobolev, Besov and Triebel-Lizorkin spaces on rough sets, J. Funct. Anal. 281 (2021), 109019, https://doi.org/10.1016/j.jfa.2021.109019.

47. (with S. N. Chandler-Wilde, A. Gibbs, D. P. Hewett and A. Moiola) A Hausdorff-measure boundary element method for acoustic scattering by fractal screens, Numerische Mathematik, to appear.

48. (with S. N. Chandler-Wilde, X. Claeys, A. Gibbs, D. P. Hewett, A. Moiola) Integral equation methods for acoustic scattering by fractals, submitted.