Weighted estimates for solutions of the ∂\partial -equation for lineally convex domains of finite type and applications to weighted bergman projections

In this paper we obtain sharp weighted estimates for solutions of the $\partial$-equation in a lineally convex domains of finite type. Precisely we obtain estimates in spaces of the form L p ({\Omega},$\delta$ $\gamma$), $\delta$ being the distance to the boundary, with gain on the index p and the exponent $\gamma$. These estimates allow us to extend the L p ({\Omega},$\delta$ $\gamma$) and lipschitz regularity results for weighted Bergman projection obtained in [CDM14b] for convex domains to more general weights

Estimates for some Weighted Bergman Projections

In this paper we investigate the regularity properties of weighted Bergman projections for smoothly bounded pseudo-convex domains of finite type in $\mathbb{C}^{n}$. The main result is obtained for weights equal to a non negative rational power of the absolute value of a special defining function $\rho$ of the domain: we prove (weighted) Sobolev-$L^{p}$ and Lipchitz estimates for domains in $\mathbb{C}^{2}$ (or, more generally, for domains having a Levi form of rank $\geq n-2$ and for "decoupled" domains) and for convex domains. In particular, for these defining functions, we generalize results obtained by A. Bonami & S. Grellier and D. C. Chang & B. Q. Li. We also obtain a general (weighted) Sobolev-$L^{2}$ estimate.Comment: Final version. To appear in Complex Variables and Elliptic Equation

Estimates for the Bergman and Szegö projections for pseudoconvex domains of finite type with locally diagonalizable Levi form

In this paper, we give precise isotropic and non-isotropic estimates for the Bergman and Szegö projections of a bounded pseudoconvex domain whose boundary points are all of finite type and with locally diagonalizable Levi form. Additional local results on estimates of invariant metrics are also given

Extremal Bases, Geometrically Separated Domains and Applications

We introduce the notion of extremal basis of tangent vector fields at a boundary point of finite type of a pseudo-convex domain in $\mathbb{C}^n$. Then we define the class of geometrically separated domains at a boundary point, and give a description of their complex geometry. Examples of such domains are given, for instance, by locally lineally convex domains, domains with locally diagonalizable Levi form, and domains for which the Levi form have comparable eigenvalues at a point. Moreover we show that these domains are localizable. Then we define the notion of "adapted pluri-subharmonic function" to these domains, and we give sufficient conditions for his existence. Then we show that all the sharp estimates for the Bergman ans Szeg\"o projections are valid in this case. Finally we apply these results to the examples to get global and local sharp estimates, improving, for examlple, a result of Fefferman, Kohn and Machedon on the Szeg\"o projection.Comment: 37 pages. Final version to appear in St. Petersburg Math.

Approximation par des fonctions holomorphes a croissance controleé

Let $\Omega$ be a bounded pseuco-convex domain in $\Bbb C^n$ with a \Cal C^{\infty} boundary, and let $S$ be the set of strictly pseudo-convex points of $\partial\Omega$. In this paper, we study the asymptotic behaviour of holomorphic functions along normals arising from points of $S$. We extend results obtained by M. Ortel and W. Schneider in the unit disc and those of A. Iordan and Y. Dupain in the unit ball of $\Bbb C^n$. We establish the existence of holomorphic functions of given growth having a "prescribed behaviour" on almost all normals arising from points of $S$

Linking local people's perception of wildlife and conservation to livelihood and poaching alleviation : a case study of the Dja biosphere reserve, Cameroon

This Paper examines how people's livelihoods and perceptions of wildlife are related to self-reported poaching (here defined as commercial bushmeat hunting) in 25 villages at the northern buffer zone of the Dja Biosphere Reserve, East Cameroon. Using a six-point Likert scale questionnaire among 263 households interviewed form March to June 2017, the following hypothesis were tested: (1) Households with positive perceptions of wildlife are less involved in poaching; (2) Positive perceptions of wildlife are linked to sustainable livelihood improvement of households; and (3) Sustainable livelihood improvement of households leads to poaching alleviation. The study area has been the site since 2010 for a community-centered conservation Program that aims to improve local peoples livelihoods (through the creation of income sources based on cocoa-based agroforestry and Non Timber Forest Products (NTFPs) Valorization) and their perceptions of wildlife (mainly through awareness raising and wildlife education) and therefore divert them from poaching. The main findings of the study indicates that positive perceptions of wildlife are linked to lower levels of poaching. Similarly, positive perception of wildlife was positively related to Livelihood improvement of the respondents. However, livelihood improvement alone did not predict poaching alleviation though we reported a significant difference in poaching frequencies of cocoa and non-cocoa producers with the firsts less involved in poaching. The findings of this study recommend more holistic approaches of biodiversity conservation that integrate simultaneously perception and livelihood improvement

The Science of Running

Running is the most primitive of all types of muscular activity. It is man's oldest racial movement. The effects of running are physiologically more far-reaching than any other form of physical activity. Running does not overdevelop or hyper-trophy any muscular groups. It normally develops in the safest way the very dynamos of life, the heart, lungs and vascular system. Running awakens the most primitive urges and joys of life, because there still exist in the neurones of man the remnants of his ancestral flights in chasing, hunting and catching. When youth and man run they wildly and joyously recapitulate the story of their long distant past. The recorded history of the art shows Pheidippides, the greatest runner of all time, performing a deed unbeatable up to modern times. Two great athletic deeds he is honoured with. Not only did he run from Athens to Sparta in two days, a distance of 152 miles, but he bore the message of the Greeks' victory over the Persians from the battlefield of Marathon to the City of Athens. It is not recorded in what time he did this 26 miles, but the distance was run so swiftly that it was the cause of his death, for he only had time to utter the words " Rejoice, we conquer " and he collapsed