Research Interests

I started my research career working in the area of function spaces, including Banach function spaces and Sobolev-type 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. The topics in harmonic analysis I have been working on include linear and multilinear singular integrals, multipliers, maximal functions and weighted inequalities.

Publications and Preprints

Local bounds for singular Brascamp-Lieb forms with cubical structure (with P. Durcik and C. Thiele), preprint. [arXiv]

Bilinear maximal functions associated with surfaces (with J. Chen, L. Grafakos, D. He and P. Honzík), Proc. Amer. Math. Soc., to appear.

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]