Bmo-type Norms Related to the Perimeter of Sets
نویسندگان
چکیده
In this paper we consider an isotropic variant of the BMO-type norm recently introduced in [6]. We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions.
منابع مشابه
Perimeter of sets and BMO-type norms
Article history: Received 10 July 2014 Accepted 10 July 2014 Available online xxxx Presented by Haïm Brezis The aim of this note is to announce some recent results showing that an isotropic variant of the BMO-type norm introduced in [3] can be related via a precise formula to the perimeter of sets. © 2014 Published by Elsevier Masson SAS on behalf of Académie des sciences.
متن کاملBruch's Membrane Opening Minimum Rim Width Measurement with SD-OCT: A Method to Correct for the Opening Size of Bruch's Membrane
A precise evaluation of the retinal nerve fiber layer thickness (RNFLT) is key for diagnosing and monitoring glaucoma. The Bruch's membrane opening minimum rim width (BMO-MRW) has been proposed as a reproducible assessment of the optic nerve. The BMO-MRW measures the minimum distance from the BMO to the internal limiting membrane. We propose an approach to correct the BMO-MRW using the BMO size...
متن کاملMeasurement of Morphological Characteristics of Raw Cane Sugar Crystals Using Digital Image Analysis
Raw cane sugar is one of the most important product in the sugar industry and is the main raw material for the white sugar production. Morphological and physical properties of this product might influence the final white sugar. For instance, the behavior during centrifugation, transport and storage is related to the characteristics of these crystals. The object of this study was to determine th...
متن کاملar X iv : 0 80 5 . 01 58 v 1 [ m at h . FA ] 1 M ay 2 00 8 OPERATOR - VALUED DYADIC BMO SPACES
We consider BMO spaces of operator-valued functions, among them the space of operator-valued functions B which define a bounded paraproduct on L(H). We obtain several equivalent formulations of ‖πB‖ in terms of the norm of the ”sweep” function of B or of averages of the norms of martingales transforms of B in related spaces. Furthermore, we investigate a connection between John-Nirenberg type i...
متن کاملA Variation on a Theme of Caffarelli and Vasseur
Recently, using DiGiorgi-type techniques, Caffarelli and Vasseur [1] showed that a certain class of weak solutions to the drift diffusion equation with initial data in L gain Hölder continuity provided that the BMO norm of the drift velocity is bounded uniformly in time. We show a related result: a uniform bound on BMO norm of a smooth velocity implies uniform bound on the C norm of the solutio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015