# LENKASLAVÍKOVÁ

# 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]