Este artículo ofrece una meta-lectura (una interpretación de distintas interpretaciones) de la identidad filosófica de Bruno Latour. Se centra la discusión en tres tipos de interpretaciones: críticas, defensas y auto-definiciones del autor. Más allá de la simpatía o el rechazo a su filosofía, se argumenta que las complejidades del pensador francés se resisten a ser categorizadas con etiquetas unívocas o ser diseccionadas analíticamente. Con base en la reformulación de la crítica propuesta por el autor, se sugiere la «hibridación antagónica» como carta de navegación para comprender adecuadamente las redes y ensamblajes que compusieron a Bruno Latour en tanto filósofo.
We prove a limited range, off-diagonal extrapolation theorem that generalizes a number of results in the theory of Rubio de Francia extrapolation, and use this to prove a limited range, multilinear extrapolation theorem. We give two applications of this result to the bilinear Hilbert transform. First, we give sufficient conditions on a pair of weights w1,w2 for the bilinear Hilbert transform to satisfy weighted norm inequalities of the form (Formula presented.),where w= ww and 1p=1p1+1p2<32. This improves the recent results of Culiuc et al. by increasing the families of weights for which this inequality holds and by pushing the lower bound on p from 1 down to 23, the critical index from the unweighted theory of the bilinear Hilbert transform. Second, as an easy consequence of our method we obtain that the bilinear Hilbert transform satisfies some vector-valued inequalities with Muckenhoupt weights. This reproves and generalizes some of the vector-valued estimates obtained by Benea and Muscalu in the unweighted case. We also generalize recent results of Carando, et al. on Marcinkiewicz-Zygmund estimates for multilinear Calderón-Zygmund operators. ; The rst author is supported by NSF Grant DMS-1362425 and research funds from the Dean of the College of Arts & Sciences, University of Alabama. The second author acknowledges nancial support from the Spanish Ministry of Economy and Competitiveness, through the \Severo Ochoa" Programme for Centres of Excellence in R&D (SEV-2015-0554). He also acknowledges that the research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ ERC agreement no. 615112 ; Peer Reviewed
We compute the right and left democracy functions of admissible wavelet bases in variable Lebesgue spaces de ned on Rn. As an application we give Lebesgue type inequalities for these wavelet bases. We also show that our techniques can be easily modi ed to prove analogous results for weighted variable Lebesgue spaces and variable exponent Triebel-Lizorkin spaces. ; The first author is supported by the Stewart-Dorwart faculty development fund at Trinity College and NSF grant 1362425. The second and third authors are supported in part by MINECO Grant MTM2010-16518 (Spain). The third author has been also supported by ICMAT Severo Ochoa project SEV-2011-0087 (Spain) and he also acknowledges that the research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ ERC agreement no. 615112 HAPDEGMT ; Peer reviewed
We study the Kato problem for divergence form operators whose ellipticity may be degenerate. The study of the Kato conjecture for degenerate elliptic equations was begun by Cruz-Uribe and Rios (2008, 2012, 2015). In these papers the authors proved that given an operator L = -wdiv(A∇) where w is in the Muckenhoupt class A and A is a w-degenerate elliptic measure (that is, A = wB with B(x) an n×n bounded, complex-valued, uniformly elliptic matrix), then L satisfies the weighted estimate ‖√Lwf‖L(w)≈‖∇f‖L(w)˙ In the present paper we solve the L-Kato problem for a family of degenerate elliptic operators. We prove that under some additional conditions on the weight w, the following unweighted L-Kato estimates hold:‖L f‖L(ℝ)˙This extends the celebrated solution to the Kato conjecture by Auscher, Hofmann, Lacey, McIntosh,and Tchamitchian, allowing the differential operator to have some degree of degeneracy in its ellipticity.For example, we consider the family of operators L=-|x| div(|x|B(x)∇), where B is any bounded,complex-valued, uniformly elliptic matrix. We prove that there exists ε > 0, depending only on dimension and the ellipticity constants, such that‖L f ‖L(ℝ),-ε<γ< 2n/n+2˙The case γ= 0 corresponds to the case of uniformly elliptic matrices. Hence, our result gives a range of γ's for which the classical Kato square root proved in Auscher et al. (2002) is an interior point. Our main results are obtained as a consequence of a rich Calderón-Zygmund theory developed for certain operators naturally associated with L. These results, which are of independent interest, establish estimates on L(w) and also on L(v dw) with v ∈ A(w), for the associated semigroup, its gradient, the functional calculus, the Riesz transform, and vertical square functions. As an application, we solve some unweighted L-Dirichlet, regularity and Neumann boundary value problems for degenerate elliptic operators. ; The first author is supported by NSF grant 1362425 and research funds provided by the Dean of Arts & Sciences at the University of Alabama. While substantial portions of this work was done he was supported by the Stewart-Dorwart faculty development fund at Trinity College. The second authors acknowledges fi nancial support from the Spanish Ministry of Economy and Competitiveness, through the \Severo Ochoa Programme for Centres of Excellence in R&D" (SEV-2015-0554). He also acknowledges that the research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ ERC agreement no. 615112 HAPDEGMT. The third author is supported by the Natural Sciences and Engineering Research Council of Canada Discovery Grant RT733901. ; Peer Reviewed
