Bochner-Riesz means at the critical index: Weighted and sparse bounds

We consider Bochner-Riesz means on weighted $L^p$ spaces, at the critical index $\lambda(p)=d(\frac 1p-\frac 12)-\frac 12$. For every $A_1$-weight we obtain an extension of Vargas' weak type $(1,1)$ inequality in some range of $p>1$. To prove this result we establish new endpoint results for sparse domination. These are almost optimal in dimension $d=2$; partial results as well as conditional results are proved in higher dimensions. For the means of index $\lambda_*=\frac{d-1}{2d+2}$ we prove fully optimal sparse bounds.Comment: 39 pages, 1 figur

Scaling agile on large enterprise level – systematic bundling and application of state of the art approaches for lasting agile transitions

International audienceOrganizations are looking for ways of establishing agile and lean process for delivery. Many approaches exist in the form of frameworks, methods and tools to setup an individual composition for a best fit. The challenge is that large organizations are heterogeneous and diverse, and hence there is no "one size fits all" approach. To facilitate a systematic implementation of agile and lean, this article proposes a transition kit based on abstraction. This kit scouts and bundles state of the art methods and tools from the agile and lean community to align them with governance and compliance aspects of the specific enterprise. Coaching of the application of the transition kit ensures an adequate instantiation. The instantiation handles business domain specific aspects and standards. A coaching governance ensures continuous improvement. An example of the systematic application of the transition approach as well as its scaling is demonstrated through its application in the Volkswagen Group IT

Sparse domination via the helicoidal method

Using exclusively the localized estimates upon which the helicoidal method was built, we show how sparse estimates can also be obtained. This approach yields a sparse domination for multiple vector-valued extensions of operators as well. We illustrate these ideas for an $n$-linear Fourier multiplier whose symbol is singular along a $k$-dimensional subspace of $\Gamma=\lbrace \xi_1+\ldots+\xi_{n+1}=0 \rbrace$, where $k<\dfrac{n+1}{2}$, and for the variational Carleson operator.Comment: 60 page

Gold transport in aqueous versus organic fluids: Experimental data and natural observations for describing ore-forming systems

The common association of carbonaceous matter (CM) with ore deposits is poorly understood. To understand the Au ore + CM association the ability of liquid hydrocarbons to act as an ore fluid was determined experimentally, and via analysis and textural observations of CMrich samples from the AuHg McLaughlin deposit in California, USA. Experimental data suggest that, below ~200 °C hydrocarbon (Au) ore fluids may be more effective transporters of Au than aqueous ore fluids

Endpoint sparse domination for classes of multiplier transformations

We prove endpoint results for sparse domination of translation invariant multiscale operators. The results are formulated in terms of dilation invariant classes of Fourier multipliers based on natural localized $M^{p\to q}$ norms which express appropriate endpoint regularity hypotheses. The applications include new and optimal sparse bounds for classical oscillatory multipliers and multi-scale versions of radial bump multipliers.Comment: 55 pages, 1 figur

Characterization of matrix valued BMO by commutators and sparse domination of operators

In the first part of this thesis, we characterize the space of matrix-valued, two-parameters BMO functions by using commutators with the Hilbert transform. The second part deals with domination of certain operators, by using a class of positive forms which have better boundedness properties and are highly localized. We present a sparse version of the T1 Theorem of David and Journé, the sparse control of a discrete version of the Hilbert transform with an oscillatory term with a quadratic phase, and the sparse domination of the Bochner-Riesz multipliers.Ph.D

Intersectional Challenges to Cohesion?:On Marginalization in an Inclusive Society

From different academic perspectives, the volume highlights realities of life and experiences of people in a diverse society on an individual, social, and political level, which are related to their ascribed non-normativity. The book combines different research approaches and results on intersectionality and marginalization discussing their relation to social cohesion. It contributes to a better understanding of how marginalized groups are marked as »not belonging« based on multiple dimensions and are systematically excluded in terms of participation and other democratic principles

Brain morphological and functional correlates of genetic, psychological, prenatal and prodromal risk for major mental disorders and their behavioural links

Cross-sectional mri-studies comparing psychiatric patients with healthy individuals have shown that patients show brain morphometric as well as functional changes. However, it is unclear whether these are pathological factors or whether these neurobiological changes are simply a risk factor for mental disorders, a consequence of therapy, only occur in certain subgroups. Therefore, the influence of a broad spectrum of different risk factors for mental disorders on brain morphometry as well as function was investigated in the present study: polygenic risk scores for psychiatric disorders, temporal perspective, shortened prenatal development as well as an extremely high risk for the development of psychosis. It can be shown that these risk factors significantly influence brain structural parameters as well as brain function. Some of these changes also correlated with behavioural changes such as poorer cognitive performance. These behavioural correlates could be valuable diagnostic or prognostic markers and could also be important research targets for the development of new therapeutic approaches