Hardy-littlewood极大函数
WebFeb 7, 2024 · We present a review of the existing stability results for Sobolev, Hardy-Littlewood-Sobolev (HLS) and related inequalities. We also contribute to the topic with some observations on constructive stability estimates for (HLS). Subjects: Analysis of PDEs (math.AP); Functional Analysis (math.FA) MSC classes: 49J40. Cite as: … WebMaximal functions appear in many forms in harmonic analysis (an area of mathematics).One of the most important of these is the Hardy–Littlewood maximal function.They play an important role in understanding, for example, the differentiability properties of functions, singular integrals and partial differential equations.
Hardy-littlewood极大函数
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Web1.2. The Hardy-Littlewood Maximal Operator and the Strong Maximal Operator The Hardy-Littlewood maximal operator and its variants, along with so-called square functions and singular integrals, form the central objects of study in har-monic analysis [12]. It is de ned as follows. De nition. Let fbe a locally integrable function on Rd. The ... 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 …
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 …
WebMay 15, 2024 · Hardy–Littlewood–Sobolev inequality on Heisenberg group. Frank and Lieb in [24] classify the extremals of this inequality in the diagonal case. This extends the earlier work of Jerison and Lee for sharp constants and extremals for the Sobolev inequality on the Heisenberg group in the conformal case in their study of CR Yamabe problem [34–36]. Web一个月前，某个无良学长扔给我一道实变题，奈何当时笔者毫无实变函数基础，题都读不懂。开学后才难得有时间学一点点，今天就来处理一下这个“历史遗留问题”！ 命题： 对于 1
Web参考: Real Analysis, SteinSingular Integrals and Differentiability Properties of Functions, Elias M. Stein关于另一种形式的极大函数(规定球心), 见Folland, Real Analysis 3.4, 视频播 …
<\infty ，存在常数 C_p 满足… third largest countryWebThe 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. … third largest mountain in the worldWebJun 5, 2024 · The Hardy–Littlewood theorem on a non-negative summable function. A theorem on integral properties of a certain function connected with the given one. It was established by G.H. Hardy and J.E. Littlewood . Let $ f $ be a non-negative summable function on $ [ a, b] $, and let third largest of its kind jumbleWebHARMONIC ANALYSIS PIOTR HAJLASZ 1. Maximal function For a locally integrable function f2L1 loc (R n) the Hardy-Littlewood max- imal function is de ned by Mf(x) = sup r>0 Z B(x;r) jf(y)jdy; x2Rn: The operator Mis not linear but it is subadditive. third largest natural harbor in the worldWebLu and Tao [14] derived the Hardy-Littlewood-Sobolev inequality for all critical indices when n− 1 n 1 p + 1 q − α +β − 1 n = 1. Furthermore, Chen, Liu, Lu and Tao [13] extended it to the weighted Hardy-Littlewood-Sobolev inequality. In the case α + β > 1, Liu [51] generalized the Hardy-Littlewood-Sobolev inequality with third largest river in indiaThis 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 third largest stock exchangeWebshowed that the set of exceptions to Littlewood’s con-jecture has Hausdorff dimension zero. 5. Waring’s Problem and the Development of theCircleMethod The circle method originates with Ramanujan as can be seen by entries of his first letter to G H Hardy in 1913 (see for example, (1.14) on page 8 of [10] as well as Selberg [11]). third largest stock exchange in us