# Kristina Ana ŠkrebUniversity of Zagreb · Department of Mathematics

Kristina Ana Škreb

PhD

## About

14

Publications

2,243

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67

Citations

Citations since 2016

Introduction

**Skills and Expertise**

## Publications

Publications (14)

The convex body maximal operator is a natural generalization of the Hardy–Littlewood maximal operator. In this paper we are considering its dyadic version in the presence of a matrix weight. To our surprise it turns out that this operator is not bounded. This is in a sharp contrast to a Doob's inequality in this context. At first, we show that the...

We present a fundamentally new proof of the dimensionless Lp boundedness of the Bakry Riesz vector on manifolds with bounded geometry. Our proof has the significant advantage that it allows for a much stronger conclusion than previous arguments, namely that of some new dimensionless weighted estimates with optimal exponent. Part of the importance o...

Morphodynamic changes in the riverbed may be accelerated by the climate change-induced effects, mostly through the increase of the frequency of extreme climatic events such as floods. This can lead to scouring of the riverbed around the bridge substructure and consequently reduces its overall stability. In order to better understand hydromorphologi...

The convex body maximal operator is a natural generalisation of the Hardy Littlewood maximal operator. In the presence of a matrix weight it is not bounded.

We prove a bi-sublinear embedding for semigroups generated by non-smooth complex-coefficient elliptic operators in divergence form and for certain mutually dual pairs of Orlicz-space norms. This generalizes a result by Carbonaro and Dragi\v{c}evi\'{c} from power functions to more general Young functions that still behave like powers. To achieve thi...

We prove an $L^p(\Omega)\times L^q(\Omega)\times L^r(\Omega)\rightarrow L^1(\Omega\times (0,\infty))$ embedding for triples of elliptic operators in divergence form with complex coefficients and subject to mixed boundary conditions on $\Omega$, and for triples of exponents $p,q,r\in(1,\infty)$ mutually related by the identity $1/p+1/q+1/r=1$. Here...

We prove failure of the natural formulation of a matrix weighted bilinear Carleson embedding theorem, featuring a matrix–valued Carleson sequence as well as products of norms for the embedding. We show that assuming an A2 weight is also not sufficient. Indeed, a uniform bound on the conditioning number of the matrix weight is necessary and sufficie...

We prove failure of the natural formulation of a matrix weighted bilinear Carleson embedding theorem, featuring a matrix valued Carleson sequence as well as products of norms for the embedding. We show that assuming an A2 weight is also not sufficient. Indeed, a uniform bound on the conditioning number of the matrix weight is necessary and sufficie...

In this paper we study cubic averages with respect to $d$ general commuting transformations and prove quantitative results on their convergence in the norm. The approach we are using is based on estimates for certain entangled multilinear singular integral forms, established recently by Durcik and Thiele.

We give an explicit formula for one possible Bellman function associated with the L p boundedness of dyadic paraproducts regarded as bilinear operators or trilinear forms. Then we apply the same Bellman function in various other settings, to give self-contained alternative proofs of the estimates for several classical operators. These include the m...

In this paper we study double ergodic averages with respect to two general commuting transformations and establish quantitative results on their convergence in the norm. In particular we estimate the number of $\varepsilon$-fluctuations in the $L^2$ norm of the sequence of ergodic averages by $\varepsilon^{-\alpha}$ for $\alpha>8$. We approach the...

In this paper we introduce a variant of Burkholder's martingale transform
associated with two martingales with respect to different filtrations. Even
though the classical martingale techniques cannot be applied, we show that the
discussed transformation still satisfies some expected $\mathrm{L}^p$
estimates. Then we apply the obtained inequalities...

When talking about large infrastructure projects one can often hear - “it is a very complex project”. What does it mean? What makes large infrastructure projects complex? This paper is exploring current views on project complexity and its development though history. As part of the research on large infrastructure projects, the perception and elemen...

The purpose of this note is to construct stochastic integrals
$\int_{0}^{t}H_s d(X_s Y_s)$ associated with two $\mathrm{L}^4$ martingales
$(X_s)_{s\geq 0}$ and $(Y_s)_{s\geq 0}$ with respect to a particular choice of
different filtrations. The process $(X_s Y_s)_{s\geq 0}$ is shown to be a "good
integrator", although it is not necessarily a semimar...