Lenka Slav'ikov'a

activity

20132022

s \to 0^{+}

of fractional Orlicz-Sobolev spaces

4 citations · 7 across the 7 of their papers we have counts for

collaborators

14 papers

math.FA2022

Boundedness of functions in fractional Orlicz-Sobolev spaces

Angela Alberico, Andrea Cianchi, Luboš Pick +1

A necessary and sufficient condition for fractional Orlicz-Sobolev spaces to be continuously embedded into $L^{\infty} (R^{n})$ is exhibited. Under the same assumption, any func…

math.CA2021

Local bounds for singular Brascamp-Lieb forms with cubical structure

Polona Durcik, Lenka Slavíková, Christoph Thiele

We prove a range of $L^{p}$ bounds for singular Brascamp-Lieb forms with cubical structure. We pass through sparse and local bounds, the latter proved by an iteration of Fourier expa…

math.CA2020

A sharp variant of the Marcinkiewicz theorem with multipliers in Sobolev spaces of Lorentz type

Loukas Grafakos, Mieczysław Mastyło, Lenka Slavíková

Given a bounded measurable function $σ$ on $R^{n}$ , we let $T_{σ}$ be the operator obtained by multiplication on the Fourier transform by $σ$ . Let $0<s_1\le s_2\le \cdots \le…

math.FA2020★ 4 cited

On the limit as $s \to 0^{+}$ of fractional Orlicz-Sobolev spaces

Angela Alberico, Andrea Cianchi, Luboš Pick +1

An extended version of the Maz'ya-Shaposhnikova theorem on the limit as $s \to 0^{+}$ of the Gagliardo-Slobodeckij fractional seminorm is established in the Orlicz space setting. Our…

math.FA2020

Fractional Orlicz-Sobolev embeddings

Angela Alberico, Andrea Cianchi, Luboš Pick +1

The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz-Sobolev spaces in $R^{n}$ . An improved embedding with an Orlicz-Lorentz target space, w…

math.CA2019

Bilinear Fourier multipliers and the rate of decay of their derivatives

Lenka Slavíková

We investigate two types of boundedness criteria for bilinear Fourier multiplier operators with symbols with bounded partial derivatives of all (or sufficiently many) orders. Theor…

math.CA2018

On the failure of the Hörmander multiplier theorem in a limiting case

Lenka Slavíková

We discuss the Hörmander multiplier theorem for $L^{p}$ boundedness of Fourier multipliers in which the multiplier belongs to a fractional Sobolev space with smoothness $s$ . We show…

math.CA2018★ 1 cited

$L^{2} \times L^{2} \to L^{1}$ boundedness criteria

Loukas Grafakos, Danqing He, Lenka Slavíková

We obtain a sharp $L^{2} \times L^{2} \to L^{1}$ boundedness criterion for a class of bilinear operators associated with a multiplier given by a signed sum of dyadic dilations of a given…

math.CA2017

A sharp version of the Hörmander multiplier theorem

Loukas Grafakos, Lenka Slavíková

We provide an improvement of the Hörmander multiplier theorem in which the Sobolev space $L_{s}^{r} (R^{n})$ with integrability index $r$ and smoothness index $s > n / r$ is replaced…

math.FA2015★ 1 cited

Norms supporting the Lebesgue differentiation theorem

Paola Cavaliere, Andrea Cianchi, Luboš Pick +1

A version of the Lebesgue differentiation theorem is offered, where the $L^{p}$ norm is replaced with any rearrangement-invariant norm. Necessary and sufficient conditions for a norm…

math.FA2015

Banach algebras of weakly differentiable functions

Andrea Cianchi, Luboš Pick, Lenka Slavíková

The question is addressed of when a Sobolev type space, built upon a general rearrangement-invariant norm, on an $n$ -dimensional domain, is a Banach algebra under pointwise multipl…

math.CA2015

On the necessity of bump conditions for the two-weighted maximal inequality

Lenka Slavíková

We study the necessity of bump conditions for the boundedness of the Hardy-Littlewood maximal operator $M$ from $L^{p} (v)$ into $L^{p} (w)$ , where $1 < p < \infty$ . The conditions in questi…

math.FA2013★ 1 cited

Compactness of higher-order Sobolev embeddings

Lenka Slavíková

We study higher-order compact Sobolev embeddings on a domain $Ω \subseteq R^{n}$ endowed with a probability measure $ν$ and satisfying certain isoperimetric inequality. Given…

math.FA2013

Higher-order Sobolev embeddings and isoperimetric inequalities

Andrea Cianchi, Luboš Pick, Lenka Slavíková

Optimal higher-order Sobolev type embeddings are shown to follow via isoperimetric inequalities. This establishes a higher-order analogue of a well-known link between first-order S…

Boundedness of functions in fractional Orlicz-Sobolev spaces

Local bounds for singular Brascamp-Lieb forms with cubical structure

A sharp variant of the Marcinkiewicz theorem with multipliers in Sobolev spaces of Lorentz type

On the limit as s→0+ of fractional Orlicz-Sobolev spaces

Fractional Orlicz-Sobolev embeddings

Bilinear Fourier multipliers and the rate of decay of their derivatives

On the failure of the Hörmander multiplier theorem in a limiting case

L2×L2→L1 boundedness criteria

A sharp version of the Hörmander multiplier theorem

Norms supporting the Lebesgue differentiation theorem

Banach algebras of weakly differentiable functions

On the necessity of bump conditions for the two-weighted maximal inequality

Compactness of higher-order Sobolev embeddings

Higher-order Sobolev embeddings and isoperimetric inequalities

On the limit as $s \to 0^{+}$ of fractional Orlicz-Sobolev spaces

$L^{2} \times L^{2} \to L^{1}$ boundedness criteria