Variable Hardy Spaces

We develop the theory of variable exponent Hardy spaces. Analogous to the classical theory, we give equivalent definitions in terms of maximal operators. We also show that distributions in these spaces have an atomic decomposition including a "finite" decomposition; this decomposition is more like the decomposition for weighted Hardy spaces due to Stromberg and Torchinsky than the classical atomic decomposition. As an application of the atomic decomposition we show that singular integral operators are bounded on variable Hardy spaces with minimal regularity assumptions on the exponent function

Norm inequalities for the minimal and maximal operator, and differentiation of the integral

We study the weighted norm inequalities for the minimal operator, a new operator analogous to the Hardy-Littlewood maximal operator which arose in the study of reverse Hölder inequalities. We characterize the classes of weights which govern the strong and weak-type norm inequalities for the minimal operator in the two weight case, and show that these classes are the same. We also show that a generalization of the minimal operator can be used to obtain information about the differentiability of the integral in cases when the associated maximal operator is large, and we give a new condition for this maximal operator to be weak (1,1)

Sharp norm inequalities for commutators of classical operators

We prove several sharp weighted norm inequalities for commutators of classical operators in harmonic analysis. We found suffcient Ap-bump conditions on pairs of weights (u; v) such that [b; T], b 2 BMO and T a singular integral operator (such as the Hilbert or Riesz transforms), maps Lp(v) into Lp(u). Because of the added degree of singularity, the commutators require a \double log bump" as opposed to that of singular integrals, which only require single log bumps. For the fractional integral operator I we nd the sharp one-weight bound on [b; I ], b 2 BMO, in terms of the Ap;q constant of the weight. We also prove sharp two-weight bounds for [b; I ] analogous to those of singular integrals. We prove two-weight weak type inequalities for [b; T] and [b; I ] for pairs of factored weights. Finally we construct several examples showing our bounds are sharp

Norm inequalities for the minimal and maximal operator, and differentiation of the integral

We study the weighted norm inequalities for the minimal operator, a new operator analogous to the Hardy-Littlewood maximal operator which arose in the study of reverse Hölder inequalities. We characterize the classes of weights which govern the strong and weak-type norm inequalities for the minimal operator in the two weight case, and show that these classes are the same. We also show that a generalization of the minimal operator can be used to obtain information about the differentiability of the integral in cases when the associated maximal operator is large, and we give a new condition for this maximal operator to be weak (1,1)

Weighted endpoint estimates for commutators of fractional integrals

summary:Given $\alpha$, $0<\alpha <n$, and $b\in {\mathrm BMO}$, we give sufficient conditions on weights for the commutator of the fractional integral operator, $[b,I_\alpha ]$, to satisfy weighted endpoint inequalities on $\mathbb{R}^n$ and on bounded domains. These results extend our earlier work [3], where we considered unweighted inequalities on $\mathbb{R}^n$

Sharp Weighted Estimates for Classical Operators [post-print]

See abstract at: http://www.sciencedirect.com/science/article/pii/S000187081100313

CONVERGENCE IN VARIABLE LEBESGUE SPACES

Abstract We consider the relationship in the variable Lebesgue space L p(·) (Ω) between convergence in norm, convergence in modular, and convergence in measure, for both bounded and unbounded exponent functions

The culture variable vis-à-vis anti-bribery law: a grey area in transnational corporate criminal liability

Cross-border transactions are generating corresponding globalisation of law enforcement efforts. Culture has significantly influenced the legal analysis of anti-bribery law. With the increase of transnational bribery, benefits from globalisation will be undermined unless an effective legal regime can mitigate the harm of bribery. It is perceived that corruption in China is more prevalent than in the West given its embedded place in Chinese culture. It is further alleged that Chinese multinational companies (MNCs) are taking advantage of an unlevel playing field, as they are not subject to stringently-enforced anti-bribery laws. This hypothesis creates a myriad of anti-bribery problems in terms of legislation and enforcement, which particularly manifest in China’s perceived cultural toleration of bribery. Cultural assumptions undermine the global anti-bribery regime and compromise potential collaborative anti-bribery efforts across jurisdictions in a rapidly globalizing world. The Chinese culture does not necessarily impede China’s criminalisation of paying bribes to foreign officials. It is argued that the cultural role should not be overestimated, otherwise the hazard of the ethnocentric engagement with the Chinese culture would affect the ability of foreign MNCs to integrate their global compliance programmes. Multinationals can only mitigate their exposure to criminal liability globally, provided that they comply robustly with anti-bribery laws of both home and host jurisdictions

First Detection of Leishmania major DNA in Sergentomyia (Spelaeomyia) darlingi from Cutaneous Leishmaniasis Foci in Mali

Leishmania major complex is the main causative agent of zoonotic cutaneous leishmaniasis (ZCL) in the Old World. Phlebotomus papatasi and Phlebotomus duboscqi are recognized vectors of L. major complex in Northern and Southern Sahara, respectively. In Mali, ZCL due to L. major is an emerging public health problem, with several cases reported from different parts of the country. The main objective of the present study was to identify the vectors of Leishmania major in the Bandiagara area, in Mali. Methodology/Principal Findings: An entomological survey was carried out in the ZCL foci of Bandiagara area. Sandflies were collected using CDC miniature light traps and sticky papers. In the field, live female Phlebotomine sandflies were identified and examined for the presence of promastigotes. The remaining sandflies were identified morphologically and tested for Leishmania by PCR in the ITS2 gene. The source of blood meal of the engorged females was determined using the cyt-b sequence. Out of the 3,259 collected sandflies, 1,324 were identified morphologically, and consisted of 20 species, of which four belonged to the genus Phlebotomus and 16 to the genus Sergentomyia. Leishmania major DNA was detected by PCR in 7 of the 446 females (1.6%), specifically 2 out of 115 Phlebotomus duboscqi specimens, and 5 from 198 Sergentomyia darlingi specimens. Human DNA was detected in one blood-fed female S. darlingi positive for L. major DNA. Conclusion: Our data suggest the possible involvement of P. duboscqi and potentially S. darlingi in the transmission of ZCL in Mali