Dominación sparse para conmutadores y estimaciones cuantitativas

Dada una funci ́on localmente integrable y un operador lineal T definimos el commutator [b, T ] como [b, T ]f (x) = b(x)T f (x) − T (bf )(x). En esta charla presentaremos resultados de dominación sparse para conmutadores y sus iteraciones para los casos en que T es un una integral singular rough, un operador A-Hörmander o un operador de Calderón-Zygmund. Suponiendo adicionalmente que b ∈ BMO o alguna clase análoga mostraremos la versatilidad de las técnicas de dominación sparse para obtener estimaciones cuantitativas. Esta charla está basada en trabajos conjuntos con A. Lerner, S. Ombrosi, C. P ́erez, L. Roncal y G. Ibañez-Firnkorn.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

A quantitative approach to weighted Carleson Condition

Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea in the 80's for the operator $$\mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{|Q|}\int_{Q}|f(x)|dx \qquad x\in\mathbb{R}^{n}, \, t \geq0$$ are obtained. As a consequence, some sufficient conditions for the boundedness of $\mathcal{M}$ in the two weight setting in the spirit of the results obtained by C. P\'erez and E. Rela and very recently by M.T. Lacey and S. Spencer for the Hardy-Littlewood maximal operator are derived. As a byproduct some new quantitative estimates for the Poisson integral are obtained

Increased temperature in urban ground as source of sustainable energy

This paper is part of the Proceedings of the 10th International Conference on Urban Regeneration and Sustainability (Sustainable City 2015). http://www.witconferences.comDensely urbanized areas are characterized by special microclimatic conditions with typically elevated temperatures in comparison with the rural surrounding. This phenomenon is known as the urban heat island (UHI) effect, but not restricted exclusively to the atmosphere. We also find significant warming of the urban subsurface and shallow groundwater bodies. Here, main sources of heat are elevated ground surface temperatures, direct thermal exploitation of aquifers and heat losses from buildings and other infrastructure. By measuring the shallow groundwater temperature in several European cities, we identify that heat sources and associated transport processes interact at multiple spatial and temporal scales. The intensity of a subsurface UHI can reach the values of above 4 K in city centres with hotspots featuring temperatures up to +20°C. In comparison with atmospheric UHIs, subsurface UHIs represent long-term accumulations of heat in a relatively sluggish environment. This potentially impairs urban groundwater quality and permanently influences subsurface ecosystems. From another point of view, however, these thermal anomalies can also be seen as hidden large-scale batteries that constitute a source of shallow geothermal energy. Based on our measurements, data surveys and estimated physical ground properties, it is possible to estimate the theoretical geothermal potential of the urban groundwater bodies beneath the studied cities. For instance, by decreasing the elevated temperature of the shallow aquifer in Cologne, Germany, by only 2 K, the obtained energy could supply the space-heating demand of the entire city for at least 2.5 years. In the city of Karlsruhe, it is estimated that about 30% of annual heating demand could be sustainably supplied by tapping the anthropogenic heat loss in the urban aquifer. These results reveal the attractive potential of heated urban ground as energy reservoir and storage, which is in place at many places worldwide but so far not integrated in any city energy plans.This work was supported by the Swiss National Science Foundation (SNSF) under grant number 200021L 144288, and the German Research Foundation (DFG), under grant number BL 1015/4-1

Geometry of physical dispersion relations

To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements to have predictive matter field dynamics and an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible.Comment: revised version, new section on applications added, 46 pages, 9 figure