WebFeb 1, 2024 · This statement is inspired in a new characterization of Hardy-Littlewood-Sobolev inequalities for elliptic and canceling homogeneous operators A (D) with … Web ∫ℝn∫ℝnf(x) x−y −λg(y)𝑑x𝑑y ≥N(n,λ,p)‖f‖Lp(ℝn)‖g‖Lt(ℝn ...
Sharp reversed Hardy–Littlewood–Sobolev inequality on R n
WebSep 22, 2015 · In this paper, we study some qualitative properties of Hardy-Littlewood-Sobolev type systems. The HLS type systems are categorized into three cases: critical, supercritical and subcritical. WebSep 27, 2024 · Title: Groundstates for Choquard type equations with Hardy-Littlewood-Sobolev lower critical exponent. Authors: Daniele Cassani, Jean Van Schaftingen, Jianjun Zhang. Download a PDF of the paper titled Groundstates for Choquard type equations with Hardy-Littlewood-Sobolev lower critical exponent, by Daniele Cassani and 1 … shoe body
Local Hardy-Littlewood-Sobolev inequalities for canceling elliptic ...
Sobolev's original proof of the Sobolev embedding theorem relied on the following, sometimes known as the Hardy–Littlewood–Sobolev fractional integration theorem. An equivalent statement is known as the Sobolev lemma in (Aubin 1982, Chapter 2). A proof is in (Stein, Chapter V, §1.3) harv error: no … See more In mathematics, there is in mathematical analysis a class of Sobolev inequalities, relating norms including those of Sobolev spaces. These are used to prove the Sobolev embedding theorem, giving inclusions between … See more Let W (R ) denote the Sobolev space consisting of all real-valued functions on R whose first k weak derivatives are functions in L . Here k is a non-negative integer and 1 ≤ p < ∞. The first part of the Sobolev embedding theorem states that if k > ℓ, p < n and 1 ≤ p < q < ∞ … See more If $${\displaystyle u\in W^{1,n}(\mathbf {R} ^{n})}$$, then u is a function of bounded mean oscillation and for some constant … See more The simplest of the Sobolev embedding theorems, described above, states that if a function $${\displaystyle f}$$ in See more Assume that u is a continuously differentiable real-valued function on R with compact support. Then for 1 ≤ p < n there is a constant C depending only on n and p such that See more Assume n < p ≤ ∞. Then there exists a constant C, depending only on p and n, such that See more The Nash inequality, introduced by John Nash (1958), states that there exists a constant C > 0, such that for all u ∈ L (R ) ∩ W (R ), The inequality follows from basic properties of the See more WebJan 1, 2005 · weighted hardy-littlewood-sobolev inequalities 167 F ollowing Chen, Li, and Ou’s work, Jin and Li [15] studied the symmetry of the solutions to the more general system (6). WebIn 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. [1] [2] shoe boat