Hardy-littlewood极大函数
Web接下来我们就来介绍 Hardy-Littlewood 极大函数。 回忆一下 6.1 节 Definition 6.3 中关于可积函数的定义,我们会记作 f \in L^1 ( L^p 空间是后面章节的内容),如果是在 \mathbb … <\infty ,存在常数 C_p 满足…
Hardy-littlewood极大函数
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Webthe Hardy-Littlewood conjecture [5] says that π(x;a) → ∞ as x → ∞. As in the twin prime conjecture, the Hardy-Littlewood conjecture gives the rate in which π(x;a) tends to infinity: Let WebAug 3, 2014 · Hardy-Littlewood 极大函数的可积性. 谨以此文纪念讨论班上遇到的可爱妹纸。. 在 Stein 的实分析上看到这个东西,据说是个很有用的发明。. 极大函数定义为对函数在某点附近取球平均,再对所有不同的球取上确界。. 其实细分有两种,一种是所有含该点的 …
Web(2) Hardy—Littlewood Maximal Operator. 这个是一个相当重要的拟线性算子,利用 Vitali Covering Theorem 和 Marcinkiewicz Interpolation Theorem 可以证明该算子是 L^{p} 有界 … WebJun 3, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site
WebCourse No.: 070101D05004Z Course Title:Harmonic Analysis Course Hours:80 Course Points:4 时间:周二、三 5-7节(13:30-15:10 & 15:20-16:10),2月18日–5月19日 地点:课程网站线上 考试:6月23-24日 课程网站线上大开卷 内容提… In mathematical analysis, the Hardy–Littlewood inequality, named after G. H. Hardy and John Edensor Littlewood, states that if and are nonnegative measurable real functions vanishing at infinity that are defined on -dimensional Euclidean space , then where and are the symmetric decreasing rearrangements of and , respectively. The decreasing rearrangement of is defined via the property that for all the two super-level sets
This theorem of G. H. Hardy and J. E. Littlewood states that M is bounded as a sublinear operator from the L (R ) to itself for p > 1. That is, if f ∈ L (R ) then the maximal function Mf is weak L -bounded and Mf ∈ L (R ). Before stating the theorem more precisely, for simplicity, let {f > t} denote the set {x … See more In mathematics, the Hardy–Littlewood maximal operator M is a significant non-linear operator used in real analysis and harmonic analysis. See more While there are several proofs of this theorem, a common one is given below: For p = ∞, the inequality is trivial (since the average of a … See more • Rising sun lemma See more The operator takes a locally integrable function f : R → C and returns another function Mf. For any point x ∈ R , the function Mf returns the maximum of a set of reals, namely the set of average values of f for all the balls B(x, r) of any radius r at x. Formally, See more It is still unknown what the smallest constants Cp,d and Cd are in the above inequalities. However, a result of Elias Stein about spherical maximal functions can be used to … See more
Web4 The Hardy-Littlewood Maximal Theorem 4 5 The Vitali Covering Lemma 5 6 Proof of The Hardy-Littlewood Theorem 5 7 The Generalized FTC Revisited 6 8 Proof of Hardy-Littlewood when p > 1 8 9 Some Closing Questions 10 1. 1 The Fundamental Theorem of Calculus Theorem 1.1 (The Fundamental Theorem of Calculus). If f is con- how to verify phcs insurance providerWeb摘要/Abstract. 摘要: 利用中间值法以及二进制方体的性质,得到了多线性Hardy-Littlewood极大算子 M 与局部可积函数 bj 所生成的一类极大交换子 Mb(j= 1, 2 ,…,m) 的 … orient genes lateral flow testsWeb我们考虑 Euclid 空间 Rd 上取值为 R 或 C 的函数, 并使用 Rd 上的 Lebesgue 测度. 但一些定义和结论可以推广到一般的 各向同性空间. 定义 1.1 (Hardy-Littlewood 极大函数). Rd … orient genes rapid covid 19 antigen self testWebApr 23, 2024 · In the proof that I gave in the main question above, the weak-Lp computations are there. They are just hidden behind the Hardy-Littlewood maximal estimate $\lVert Mf\rVert_p\le C \lVert f\rVert_p$, which indeed is proven via the interpolation theorem of Marcinkiewicz. orient garden boca ratonWebThe Hardy-Littlewood maximal inequality Let us work in Euclidean space Rd with Lebesgue measure; we write E instead of µ(E) for the Lebesgue measure of a set E. … orient garden royal palm beach flWebDec 1, 2024 · This is a survey article about recent developments in dimension-free estimates for maximal functions corresponding to the Hardy--Littlewood averaging … how to verify pgpWebDec 7, 2015 · In words, it means that the maximal function is not much larger than $ f $. (Stein and Shakarchi Real Analysis p.101). The lefthand side is the measure of the set of … orient genes rapid covid 19 test