Research Interests

I started my research career working in the area of function spaces. I became interested in harmonic analysis during the later part of my PhD study. At the present time I continue working in both areas, focusing in particular on their interaction. I am also interested in applications of these areas to other fields of mathematics, such as ergodic theory and partial differential equations.

Organization of Scientific Events

International Prague seminar on function spaces, an online research seminar which takes place biweekly on Tuesdays from 14:00.

Geometric and functional inequalities, function spaces and PDEs, a conference organized on the occasion of the 60th birthday of Andrea Cianchi. It took place in February 2023 in Prague.

Publications and Preprints

Boundedness criteria for bilinear Fourier multipliers via shifted square function estimates (with G. Dosidis and B. Park), preprint. [arxiv]

On the modulus of continuity of fractional Orlicz-Sobolev functions (with A. Alberico, A. Cianchi and L. Pick), preprint. [arxiv]

Dimension-free inequalities for low and high degree functions on the Hamming cube (with K. Domelevo, P. Durcik, V. Fragkiadaki, O. Klein, D. Oliveira e Silva and B. Wróbel), preprint. [arXiv]

Norm-variation of triple ergodic averages for commuting transformations (with P. Durcik and C. Thiele), preprint. [arXiv]

Multilinear singular integrals with homogeneous kernels near L¹ (with G. Dosidis), Math. Ann., to appear. [article] [arXiv]

Boundedness of functions in fractional Orlicz-Sobolev spaces (with A. Alberico, A. Cianchi and L. Pick), Nonlinear Anal. 230 (2023), Paper No. 113231, 26 pp. [article] [arXiv]

Local bounds for singular Brascamp-Lieb forms with cubical structure (with P. Durcik and C. Thiele), Math. Z. 302 (2022), 2375 - 2405. [article] [arXiv]

Bilinear maximal functions associated with surfaces (with J. Chen, L. Grafakos, D. He and P. Honzík), Proc. Amer. Math. Soc. 150 (2022), no. 4, 1635 - 1639. [article]

A sharp variant of the Marcinkiewicz theorem with multipliers in Sobolev spaces of Lorentz type (with L. Grafakos and M. Mastyło), J. Funct. Anal. 282 (2022), no. 3, Paper No. 109295. [article] [arXiv]

Fractional Orlicz-Sobolev embeddings (with A. Alberico, A. Cianchi and L. Pick), J. Math. Pures Appl. 149 (2021), 216 - 253. [article] [arXiv]

Bilinear Fourier multipliers and the rate of decay of their derivatives, J. Approx. Theory 261 (2021), 105485, 25pp. [article] [arXiv]

On the limit as s→ 1^- of possibly non-separable fractional Orlicz-Sobolev spaces (with A. Alberico, A. Cianchi and L. Pick), Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 31 (2020), no. 4, 879-899. [article]

On the limit as s → 0⁺ of fractional Orlicz-Sobolev spaces (with A. Alberico, A. Cianchi and L. Pick), J. Fourier Anal. Appl. 26 (2020), no. 6, Paper No. 80, 19 pp. [article] [arXiv]

On the failure of the Hörmander multiplier theorem in a limiting case, Rev. Mat. Iberoam. 36 (2020), no. 4, 1013 - 1020. [article] [arXiv]

Sobolev embeddings in Orlicz and Lorentz spaces with measures (with A. Cianchi and L. Pick), J. Math. Anal. Appl. 1485 (2020), no. 2, 123827. [article]

Sobolev embeddings, rearrangement-invariant spaces and Frostman measures (with A. Cianchi and L. Pick), Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 1, 105 - 144. [article] [arXiv]

L² × L² → L¹ boundedness criteria (with L. Grafakos and D. He), Math. Ann. 376 (2020), no. 1 - 2, 431 - 455. [article] [arXiv]

A sharp version of the Hörmander multiplier theorem (with L. Grafakos), Int. Math. Res. Not. IMRN 2019, no. 15, 4764 - 4783. [article][arXiv]

Banach algebras of weakly differentiable functions (with A. Cianchi and L. Pick), J. Anal. Math. 138 (2019), no. 2, 473 - 511. [article] [arXiv]

Failure of the Hörmander kernel condition for multilinear Calderón-Zygmund operators (with L. Grafakos and D. He), C. R. Math. Acad. Sci. Paris 357 (2019), no. 4, 382 - 388. [article]

The Marcinkiewicz multiplier theorem revisited (with L. Grafakos), Arch. Math. (Basel) 112 (2019), no. 2, 191 - 203. [article][arXiv]

Sharp Sobolev type embeddings on the entire Euclidean space (with A. Alberico, A. Cianchi and L. Pick), Comm. Pure Appl. Anal. 17 (2018), no. 5, 2011 - 2037. [article] [arXiv]

Norms supporting the Lebesgue differentiation theorem (with P. Cavaliere, A. Cianchi and L. Pick), Commun. Contemp. Math. 20, no. 1 (2018). [article][arXiv]

On the necessity of bump conditions for the two-weighted maximal inequality, Proc. Amer. Math. Soc. 145 (2017), 109 - 118. [article][arXiv]

Compactness of higher-order Sobolev embeddings, Publ. Mat. 59 (2015), no. 2, 373 - 448. [article][arXiv]

Higher-order Sobolev embeddings and isoperimetric inequalities (with A. Cianchi and L. Pick), Adv. Math. 273 (2015), 568 - 650. [article] [arXiv]

Almost-compact embeddings, Math. Nachr. 285 (2012), 1500 - 1516. [article]