کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4589754 1334904 2016 37 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Isoperimetric weights and generalized uncertainty inequalities in metric measure spaces
ترجمه فارسی عنوان
وزنهای ایسپری متریک و نابرابریهای نااطمینانی کلی در فضاهای اندازهگیری متریک
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

We extend the recent L1L1 uncertainty inequalities obtained in [13] to the metric setting. For this purpose we introduce a new class of weights, named isoperimetric weights  , for which the growth of the measure of their level sets μ({w≤r})μ({w≤r}) can be controlled by rI(r)rI(r), where I is the isoperimetric profile of the ambient metric space. We use isoperimetric weights, new localized Poincaré inequalities  , and interpolation, to prove Lp,1≤p<∞Lp,1≤p<∞, uncertainty inequalities on metric measure spaces. We give an alternate characterization of the class of isoperimetric weights in terms of Marcinkiewicz spaces, which combined with the sharp Sobolev inequalities of [20], and interpolation of weighted norm inequalities, give new uncertainty inequalities in the context of rearrangement invariant spaces.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 270, Issue 9, 1 May 2016, Pages 3307–3343
نویسندگان
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