Martin Kvrepela

activity

20162019

collaborators

6 papers

math.FA2019

Weighted inequalities for discrete iterated Hardy operators

Amiran Gogatishvili, Martin Křepela, Rastislav Oľhava +1

We characterize a three-weight inequality for an iterated discrete Hardy-type operator. In the case when the domain space is a weighted space $ℓ^{p}$ with $p \in (0, 1]$ , we develop…

math.AP2019

Solenoidal difference quotients and their application to the regularity theory of the $p$ -Stokes system

Martin Křepela, Michael Růžička

We prove existence of a solution to the divergence equation satisfying a new Bogovski-type estimate for the difference quotients. This enables us to give an alternative proof of th…

math.FA2018

Weighted inequalities for iterated Copson integral operators

Martin Křepela, Luboš Pick

We solve a long-standing open problem in theory of weighted inequalities concerning iterated Copson operators. We use a constructive approximation method based on a new discretizat…

math.AP2017

A counterexample related to the regularity of the $p$ -Stokes problem

Martin Křepela, Michael Růžička

In this paper we construct a solenoidal vector field $u$ belonging to $W^{2, q} (Ω) \cap W_{0}^{1, s} (Ω)$ , $s \in (1, \infty)$ , $q \in (1, n)$ , such that $(1 + ∣ Du ∣)^{p - 2}$ …

math.FA2016

Embeddings and associated spaces of Copson-Lorentz spaces

Martin Křepela

Let $m, p, q \in (0, \infty)$ and let $u, v, w$ be nonnegative weights. We characterize validity of the inequality \[ \left(\int_0^\infty w(t) (f^*(t))^q \, dt \right)^\frac 1q \le C \lef…

math.FA2016

Boundedness of Hardy-type operators with a kernel: integral weighted conditions for the case $0 < q < 1 \leq p < \infty$

Martin Křepela

Let $U : [0, \infty)^{2} \to [0, \infty)$ be a~measurable kernel satisfying: (i) $U (x, y)$ is nonincreasing in $x$ and nondecreasing in $y$ ; (ii) there exists a~constant $θ > 0$ such that $…