Hardy-littlewood-sobolev
WebSep 15, 2014 · Sobolev's inequalities and Hardy–Littlewood–Sobolev inequalities are dual. A fundamental reference for this issue is E.H. Lieb's paper [36]. This duality has also … WebOct 26, 2024 · ABSTRACT In this note, we prove the Stein–Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous norms play a key role in our proofs. Also, we give a simple proof of the Hardy–Littlewood–Sobolev inequality on general homogeneous Lie …
Hardy-littlewood-sobolev
Did you know?
WebJul 1, 2012 · In this paper, we study two types of weighted Hardy–Littlewood–Sobolev (HLS) inequalities, also known as Stein–Weiss inequalities, on the Heisenberg group. More precisely, we prove the u weighted HLS inequality in Theorem 1.1 and the z weighted HLS inequality in Theorem 1.5 (where we have denoted u = (z, t) as points on the ... WebNov 1, 2010 · We explain an interesting relation between the sharp Hardy-Littlewood-Sobolev (HLS) inequality for the resolvent of the Laplacian, the sharp Gagliardo-Nirenberg-Sobolev (GNS) inequality, and the fast diffusion equation (FDE). As a consequence of this relation, we obtain an identity expressing the HLS functional as an integral involving the …
WebMar 6, 2024 · Hardy–Littlewood–Sobolev lemma. Sobolev's original proof of the Sobolev embedding theorem relied on the following, sometimes known as the … WebIn this paper, we study a class of fast diffusion p-Laplace equation with singular potential in a bounded smooth domain with homogeneous Dirichlet boundary condition. By using energy estimates, Hardy-Littlewood-Sobolev inequality, and some ordinary differential inequalities, we get the solution of the equation exists globally. Moreover, the conditions …
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 … WebSome Hardy type inequalities on the domain in the Heisenberg group are established by using the Picone type identity and constructing suitable auxiliary functi
WebMar 28, 2014 · Groundstates of nonlinear Choquard equations: Hardy-Littlewood-Sobolev critical exponent. Vitaly Moroz, Jean Van Schaftingen. We consider nonlinear Choquard equation where , is an external potential and is the Riesz potential of order . The power in the nonlocal part of the equation is critical with respect to the Hardy-Littlewood …
WebAbstract. We prove that the Hardy-Littlewood maximal operator is bounded in the Sobolev space W 1,p ( R n) for 1< p ≤∞. As an application we study a weak type inequality for the Sobolev capacity. We also prove that the Hardy-Littlewood maximal function of a Sobolev function is quasi-continuous. Download to read the full article text. polystichum acrostichoides characteristicsshannon cochran actressWebApr 15, 2024 · The Hardy–Littlewood–Sobolev inequality plays an important role in studying nonlocal problems and we'd like to mention that other nonlocal version inequalities are considered in some recent literature, for example, the authors in [25] studied the Hardy–Littlewood inequalities in fractional weighted Sobolev spaces. shannon cochraneWebWe 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. shannon cockerill fitWebHARDY-LITTLEWOOD-SOBOLEV INEQUALITY 3 By interchanging summation and integral, we have Z f X 2k−1≤ f 2k(p−1) ∼ Z f · f p−1 = kfkp p. So, kMfkp. kfkp. 3. Proof … polystichum acrostichoides pronunciationWebDec 1, 2024 · Gao and M. Yang, “ On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents,” J. Math. Anal. Appl. 448, 1006 ... shannon coachWebWe prove that the Hardy-Littlewood maximal operator is bounded in the Sobolev spaceW 1,p (R n) for 1 shannon cockerill