Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces

In this paper we prove T1 type necessary and sufficient conditions for the boundedness on inhomogeneous Lipschitz spaces of fractional integrals and singular integrals defined on a measure metric space whose measure satisfies a n-dimensional growth. We also show that hypersingular integrals are bounded on these spaces.

Net spaces and boundedness of integral operators

In this paper we introduce new functional spaces which we call the net spaces. Using their properties, the necessary and sufficient conditions for the integral operators to be of strong or weak-type are obtained. The estimates of the norm of the convolution operator in weighted Lebesgue spaces are presented.

Use of a human-like low-grade bacteremia model of experimental endocarditis to study the role of Staphylococcus aureus adhesins and platelet aggregation in early endocarditis.

Animal models of infective endocarditis (IE) induced by high-grade bacteremia revealed the pathogenic roles of Staphylococcus aureus surface adhesins and platelet aggregation in the infection process. In humans, however, S. aureus IE possibly occurs through repeated bouts of low-grade bacteremia from a colonized site or intravenous device. Here we used a rat model of IE induced by continuous low-grade bacteremia to explore further the contributions of S. aureus virulence factors to the initiation of IE. Rats with aortic vegetations were inoculated by continuous intravenous infusion (0.0017 ml/min over 10 h) with 10(6) CFU of Lactococcus lactis pIL253 or a recombinant L. lactis strain expressing an individual S. aureus surface protein (ClfA, FnbpA, BCD, or SdrE) conferring a particular adhesive or platelet aggregation property. Vegetation infection was assessed 24 h later. Plasma was collected at 0, 2, and 6 h postinoculation to quantify the expression of tumor necrosis factor (TNF), interleukin 1α (IL-1α), IL-1β, IL-6, and IL-10. The percentage of vegetation infection relative to that with strain pIL253 (11%) increased when binding to fibrinogen was conferred on L. lactis (ClfA strain) (52%; P = 0.007) and increased further with adhesion to fibronectin (FnbpA strain) (75%; P < 0.001). Expression of fibronectin binding alone was not sufficient to induce IE (BCD strain) (10% of infection). Platelet aggregation increased the risk of vegetation infection (SdrE strain) (30%). Conferring adhesion to fibrinogen and fibronectin favored IL-1β and IL-6 production. Our results, with a model of IE induced by low-grade bacteremia, resembling human disease, extend the essential role of fibrinogen binding in the initiation of S. aureus IE. Triggering of platelet aggregation or an inflammatory response may contribute to or promote the development of IE.

Sharp A₂ inequality for haar shift operators

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Sharp weighted bounds for fractional integral operators

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.

Heterogeneous dynamics, aggregation and the persistence of economic shocks

It has been recently emphasized that, if individuals have heterogeneous dynamics, estimates of shock persistence based on aggregate data are significatively higher than those derived from its disaggregate counterpart. However, a careful examination of the implications of this statement on the various tools routinely employed to measure persistence is missing in the literature. This paper formally examines this issue. We consider a disaggregate linear model with heterogeneous dynamics and compare the values of several measures of persistence across aggregation levels. Interestingly, we show that the average persistence of aggregate shocks, as measured by the impulse response function (IRF) of the aggregate model or by the average of the individual IRFs, is identical on all horizons. This result remains true even in situations where the units are (short-memory) stationary but the aggregate process is long-memory or even nonstationary. In contrast, other popular persistence measures, such as the sum of the autoregressive coefficients or the largest autoregressive root, tend to be higher the higher the aggregation level. We argue, however, that this should be seen more as an undesirable property of these measures than as evidence of different average persistence across aggregation levels. The results are illustrated in an application using U.S. inflation data.

(Optimal) Spatial Aggregation in the Determinants of Industrial Location

Empirical studies on the determinants of industrial location typically use variables measured at the available administrative level (municipalities, counties, etc.). However, this amounts to assuming that the effects these determinants may have on the location process do not extent beyond the geographical limits of the selected site. We address the validity of this assumption by comparing results from standard count data models with those obtained by calculating the geographical scope of the spatially varying explanatory variables using a wide range of distances and alternative spatial autocorrelation measures. Our results reject the usual practice of using administrative records as covariates without making some kind of spatial correction. Keywords: industrial location, count data models, spatial statistics JEL classification: C25, C52, R11, R30

Bergman-type singular operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball

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Weak-type estimates for Haar shift operators: Sharp power on the A(p) characteristic

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Maximal operators and differentiation theorems for sparse sets

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Lp theory for the multidimensional aggregation equation

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Two weight inequalities for discrete positive operators

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Two weight inequalities for maximal truncations of dyadic Calderón-Zygmund operators

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A Schoenflies extension theorem for a class of locally bi-Lipschitz homeomorphisms

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