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: … WebNov 28, 2014 · There is a direct and self-contained proof of HLS inequality in Analysis by Lieb and Loss, Theorem 4.3.It uses nothing but layer cake representation, Hölder's …
Hardy–Littlewood inequality - Wikipedia
WebHardy-Littlewood-Po´lya inequality are also included. 1. Introduction The Hardy-Littlewood-Po´lya theorem of majorization is an important result in convex analysis that lies at the core of majorization theory, a subject that attracted a great deal of attention due to its numerous applications in mathematics, statistics, WebWe study the Hardy–Littlewood–Sobolev inequality on mixed-norm Lebesgue spaces. We give a complete characterization of indices \vec p and \vec q such that the Riesz potential is bounded from L^ {\vec p} to L^ {\vec q}. In particular, all the endpoint cases are studied. port wentworth government
Hardy–Littlewood Inequality (Chapter 18) - Dirichlet Series …
WebDiscrete HardyLittlewood 2 and the associated function ma (c) = Ma). This is also the onedimensional measure of the intersection of the line y = c and the region {(x,y) 0 ≤ y ≤ a(x)}. y = c m(c) = 4 The functions ma and Ra are the same. 1.1. Proposition. Suppose a and b to be two nonnegative weakly decreasing arrays. The following ... WebAug 16, 2001 · Hardy-Littlewood maximal inequality By Antonios D. Melas Abstract We find the exact value of the best possible constant C for the weak-type ... The simplest example of such a maximal operator is the centered Hardy-Littlewood maximal operator defined by (1.1) Mf(x)=sup h>0 1 2h x+h x−h f for every f ∈ L1(R ). WebIn this paper, first we present some interesting identities associated with Green’s functions and Fink’s identity, and further we present some interesting inequalities for r-convex … irons by handicap