Affective continuities across Muslim and Christian settings in Berlin

This article, a reflection on collaborative fieldwork involving a Sufi Muslim and a Pentecostal Christian setting in Berlin, examines whether distinct and diverse religious groups can be brought into a meaningful relation with one another. It considers the methodological possibilities that might become possible or foreclose when two researchers, working in different prayer settings in the same city, use affect as a common frame of reference while seeking to establish shared affective relations and terrains that would otherwise be implausible. With two separately observed accounts of prayer gatherings in a shared urban context, we describe locally specific workings of affect and sensation. We argue that sense-aesthetic forms and patterns in our field sites are supralocal affective forms that help constitute an analytic relationality between the two religious settings

A Simple Approach to Functional Inequalities for Non-local Dirichlet Forms

With direct and simple proofs, we establish Poincar\'{e} type inequalities (including Poincar\'{e} inequalities, weak Poincar\'{e} inequalities and super Poincar\'{e} inequalities), entropy inequalities and Beckner-type inequalities for non-local Dirichlet forms. The proofs are efficient for non-local Dirichlet forms with general jump kernel, and also work for $L^p (p>1)$ settings. Our results yield a new sufficient condition for fractional Poincar\'{e} inequalities, which were recently studied in \cite{MRS,Gre}. To our knowledge this is the first result providing entropy inequalities and Beckner-type inequalities for measures more general than L\'{e}vy measures.Comment: 12 page

On maximal parabolic regularity for non-autonomous parabolic operators

We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to time integrability exponents $r\neq 2$. This allows us to prove maximal parabolic $L^r$-regularity for discontinuous non-autonomous second-order divergence form operators in very general geometric settings and to prove existence results for related quasilinear equations