Publications

PREPRINTS

  1. A sparse resolution of the DiPerna-Majda gap problem for 2D Euler equations. Joint work with D. Spector. 24 pp. ArXiv

  2. New approach to affine Moser-Trudinger inequalities via Besov polar projection bodies. Joint work with Y. Li, S. Tikhonov, D. Yang and W. Yuan. 34 pp. ArXiv

  3. A sharp stability criterion for Euler equations via sparseness. Joint work with M. Milman. 47 pp. ArXiv

  4. Uniqueness for 2D Euler and transport equations via extrapolation. Joint work with M. Milman. 36 pp. ArXiv
  5. Sobolev embeddings, extrapolations, and related inequalities. Joint work with S. Tikhonov. 97 pp. ArXiv

PUBLISHED/ACCEPTED

  1. A unified approach to self-improving property via K-functionals. Joint work with Y. Li, S. Tikhonov, D. Yang and W. Yuan. Calc. Var. Partial Differential Equations (to appear) ArXiv
  2. Truncated smooth function spaces. Joint work with S. Tikhonov. Trans. Amer. Math. Soc. (to appear) ArXiv
  3. Spaces of Besov–Sobolev type and a problem on nonlinear approximation. Joint work with A. Seeger, B. Street, J. Van Schaftingen and P.-L. Yung. J. Funct. Anal. 284 (2023), 50 pp. ArXiv
  4. Bourgain–Brezis–Mironescu–Maz’ya–Shaposhnikova limit formulae for fractional Sobolev spaces via interpolation and extrapolation. Joint work with M. Milman. Calc. Var. Partial Differential Equations 62 (2023), 37 pp. ArXiv
  5. New Brezis-Van Schaftingen-Yung-Sobolev type inequalities connected with maximal inequalities and one parameter families of operators. Joint work with M. Milman. Adv. Math. 411 (2022), 76 pp. ArXiv
  6. On the A_∞ condition for elliptic operators in 1-sided NTA domains satisfying the capacity density condition. Joint work with M. Cao, J.M. Martell and P. Tradacete. Forum Math. Sigma 10 (2022), 57 pp. ArXiv
  7. New estimates for the maximal functions and applications. Joint work with S. Tikhonov. Trans. Amer. Math. Soc. 375 (2022), 3969–4018 ArXiv
  8. Sparse Brudnyi and John–Nirenberg spaces. Joint work with M. Milman. Comptes Rendus Mathematique  354 (2021), 1059–1069 ArXiv
  9. Embeddings and characterizations of Lipschitz spaces. Joint work with D.D. Haroske and S. Tikhonov. J. Math. Pures Appl. 144 (2020), 69–105 ArXiv
  10. Function spaces of logarithmic smoothness: embeddings and characterizations. Joint work with S. Tikhonov. Mem. Amer. Math. Soc. 1393 (2023), 180 pp. ArXiv
  11. Extensions of the vector-valued Hausdorff-Young inequalities. Joint work with M. Veraar. Math. Z. 299 (2021), 373–425 ArXiv
  12. Approximation and entropy numbers of embeddings between approximation spaces. Joint work with F. Cobos and T. Kühn. Constr. Approx. 47 (2018), 453–486.
  13. Sharp estimates of the norms of embeddings between Besov spaces. Z. Anal. Anwend. 37 (2018), 127–149.
  14. On nuclearity of embeddings between Besov spaces. Joint work with F. Cobos and T. Kühn. J. Approx. Theory 225 (2018), 209–223.
  15. Sharp embeddings of Besov spaces with logarithmic smoothness in sub-critical cases. Analysis Math. 43 (2017), 219–240.
  16. Ul’yanov-type inequalities and embeddings between Besov spaces: the case of parameters with limit values. Math. Inequal. Appl. 20 (2017), 755–772.
  17. Tractable embeddings of Besov spaces into small Lebesgue spaces. Math. Nachr. 289 (2016), 1739–1759.
  18. On the relationship between two kinds of Besov spaces with smoothness near zero and some other applications of limiting interpolation. Joint work with F. Cobos. J. Fourier Anal. Appl. 22 (2016), 1174–1191.
  19. On Besov spaces modelled on Zygmund spaces. Joint work with F. Cobos. J. Approx. Theory 211 (2016), 61–77.
  20. Characterizations of logarithmic Besov spaces in terms of differences, Fourier-analytical decompositions, wavelets and semi-groups. Joint work with F. Cobos and H. Triebel. J. Funct. Anal. 270 (2016), 4386–4425.
  21. On Besov spaces of logarithmic smoothness and Lipschitz spaces. Joint work with F. Cobos. J. Math. Anal. Appl. 425 (2015), 71–84.
  22. Approximation spaces, limiting interpolation and Besov spaces. Joint work with F. Cobos. J. Approx. Theory 189 (2015), 43–66.
  23. Embeddings of Besov spaces of logarithmic smoothness. Joint work with F. Cobos. Studia Math. 223 (2014), 193–204.
  24. Compact operators and approximation spaces. Joint work with F. Cobos and A. Martínez. Colloq. Math. 136 (2014), 1–11.
  25. On a nonlinear boundary value problem modeling corneal shape. Joint work with L. Plociniczak, W. Okrasinski and J.J. Nieto. J. Math. Anal. Appl. 414 (2014), 461–471.
  26. Finite element approximation of nonlinear transient magnetic problems involving periodic potential drop excitations. Joint work with A. Bermúdez de Castro, D. Gómez and P. Salgado. Comput. Math. Appl. 65 (2013), 1200–1219.