作者：Omer Angel , RichÁrd Balka , AndrÁs MÁthé ... 来源：[J].Transactions of the American Mathematical Society(IF 1.019), 2018, Vol.370 (6), pp.4223-4247AMS 摘要：For $0<\alpha <1$ let $V(\alpha )$ denote the supremum of the numbers $v$ such that every $\alpha$-Hölder continuous function is of bounded variation on a set of Hausdorff dimension $v$. Kahane and Katznelson (2009) proved the estimate $1/2 \leq V(\alpha )\leq 1/(2-\a...  作者：Tuomas P. HytÖnen , Kangwei Li 来源：[J].Proceedings of the American Mathematical Society(IF 0.609), 2018, Vol.146 (6), pp.2497-2507AMS 摘要：We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main new result is the optimal bound$ [w]_{A_p}^{1/p}[w]_{A_\infty }^{1/2-1/p}\lesssim [w]_{A_p}^{1/2}$fo...  作者：V. I. Kopeiko 来源：[J].St. Petersburg Mathematical Journal(IF 0.46), 2018, Vol.29 (3), pp.447-467AMS 摘要：Transfer of the unitary$ K_1$-functor under polynomial extensions of unitary rings is constructed and composition of this transfer with the natural homomorphism induced by embedding of polynomial rings is computed. As an application of the composition formula, unitary$ K_1$-ana...  作者：Michael HrušÁk , Jan van Mill 来源：[J].Proceedings of the American Mathematical Society(IF 0.609), 2018, Vol.146 (6), pp.2689-2695AMS 摘要：We show that the existence of a countable dense homogeneous metric space which is connected and meager in itself is independent of$ \mathsf {ZFC}$.  作者：Youngwoo Koh , Ihyeok Seo 来源：[J].Proceedings of the American Mathematical Society(IF 0.609), 2018, Vol.146 (6), pp.2555-2562AMS 摘要：We obtain a unique continuation result for the differential inequality$ \vert (i\partial _t +\Delta )u \vert \leq \vert Vu\vert + \vert W\cdot \nabla u \vert$by establishing$ L^2$Carleman estimates. Here,$ V$is a scalar function and$ W$is a vector function, which may...  作者：V. Valov 来源：[J].Proceedings of the American Mathematical Society(IF 0.609), 2018, Vol.146 (6), pp.2697-2705AMS 摘要：In accordance with the Bing-Borsuk conjecture, we show that if$ X$is an$ n$-dimensional homogeneous metric$ ANR$-compactum and$ x\in X$, then there is a local basis at$ x$consisting of connected open sets$ U$such that the homological properties of$ \overline U$and$ bd...
 作者：Dragomir šarić 来源：[J].Proceedings of the American Mathematical Society(IF 0.609), 2018, Vol.146 (6), pp.2457-2471AMS 摘要：Let $X_0$ be an infinite area geodesically complete hyperbolic surface which can be decomposed into geodesic pairs of pants. We introduce Thurston's boundary to the Teichmüller space $T(X_0)$ of the surface $X_0$ using the length spectrum analogous to Thurston's construct...
 作者：Joshua Evan Greene 来源：[J].Proceedings of the American Mathematical Society(IF 0.609), 2018, Vol.146 (6), pp.2707-2709AMS 摘要：Let $L \subset S^3$ denote an alternating link and $\Sigma (L)$ its branched double-cover. We give a short proof of the fact that the fundamental group of $\Sigma (L)$ admits a left-ordering iff $L$ is an unlink. This result is originally due to Boyer-Gordon-Watson.
 作者：Christopher Lopez 来源：[J].Transactions of the American Mathematical Society(IF 1.019), 2018, Vol.370 (6), pp.4111-4145AMS 摘要：We establish fundamental results for a parabolic flow of Riemannian metrics introduced by Bahuaud-Helliwell which is based on the Fefferman-Graham ambient obstruction tensor. First, we obtain local L2 smoothing estimates for the curvature tensor and use them to prove pointwise sm...
 作者：Timothy C. Burness , Martin W. Liebeck , Aner Shalev 来源：[J].Proceedings of the American Mathematical Society(IF 0.609), 2018, Vol.146 (6), pp.2343-2358AMS 摘要：We introduce the notion of the depth of a finite group $G$, defined as the minimal length of an unrefinable chain of subgroups from $G$ to the trivial subgroup. In this paper we investigate the depth of (non-abelian) finite simple groups. We determine the simple groups of minim...