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

HCN versus HCO+ as dense molecular gas mass tracer in Luminous Infrared Galaxies

It has been recently argued that the HCN J=1--0 line emission may not be an unbiased tracer of dense molecular gas (\rm n\ga 10^4 cm^{-3}) in Luminous Infrared Galaxies (LIRGs: $\rm L_{FIR}> 10^{11} L_{\odot}$) and HCO$^+$ J=1--0 may constitute a better tracer instead (Graci\'a-Carpio et al. 2006), casting doubt into earlier claims supporting the former as a good tracer of such gas (Gao & Solomon 2004; Wu et al. 2006). In this paper new sensitive HCN J=4--3 observations of four such galaxies are presented, revealing a surprisingly wide excitation range for their dense gas phase that may render the J=1--0 transition from either species a poor proxy of its mass. Moreover the well-known sensitivity of the HCO$^+$ abundance on the ionization degree of the molecular gas (an important issue omitted from the ongoing discussion about the relative merits of HCN and HCO$^+$ as dense gas tracers) may severely reduce the HCO$^+$ abundance in the star-forming and highly turbulent molecular gas found in LIRGs, while HCN remains abundant. This may result to the decreasing HCO$^+$/HCN J=1--0 line ratio with increasing IR luminosity found in LIRGs, and casts doubts on the HCO$^+$ rather than the HCN as a good dense molecular gas tracer. Multi-transition observations of both molecules are needed to identify the best such tracer, its relation to ongoing star formation, and constrain what may be a considerable range of dense gas properties in such galaxies.Comment: 16 pages, 4 figures, Accepted for publication in the Astrophysical Journa

Molecular Gas in the Bulge and Ring of NGC 7331

Maps of the J=2-1 12CO emission from the SbII galaxy NGC 7331 show a low-contrast ring at a radius of about 3.5 kpc. There is no evidence for a pronounced central hole in the CO distribution as claimed by others. The molecular ring is just outside the radius of peak emission from warm dust, but coincides with the peak of colder dust emission. Various 12CO and 13CO transitions have been observed from three positions including the center, which was also observed in the 492 GHz transition. The line measurements have been modelled by emission from a clumpy mixture of low-density molecular gas at about T(kin) = 10 K and high-density molecular gas at temperatures of 10 K and 20 K. The CO to H2 conversion factor in NGC 7331 is lower than that in the Milky Way, and lowest in the center of NGC 7331. The total interstellar gas mass is dominated by molecular hydrogen in the bulge and in the ring, and by atomic hydrogen outside the ring. Total hydrogen mass densities in the ring are about twice those in the bulge. Total gas to dynamic mass ratios increase from 1% in the bulge to 3% outside the ring. The bulge molecular gas may have originated in mass loss from bulge stars, in which case the molecular ring is probably the consequence of evacuation efficiency decreases at the outer bulge edge.Comment: 12 pages, 4 figures, A&A in pres

A low-mass HI companion of NGC 1569?

High-sensitivity maps of the large-scale structure of atomic hydrogen in the starburst dwarf galaxy NGC 1569 show evidence for an HI cloud with a mass of 7*10**6 M_sun, at a projected distance of 5 kpc from the parent galaxy. This cloud may be a condensation in a low-column-density HI halo or a companion galaxy/HI-cloud. NGC 1569 and its companion are connected by a low surface brightness HI bridge. At the edge of NGC1569, the HI bridge coincides with H_alpha arcs, also detected in soft X-rays.Comment: 5 pages, 4 figures, 1 tabl