Results 51 to 60 of about 648,405 (147)

Existence of groundstates for Choquard type equations with Hardy–Littlewood–Sobolev critical exponent

Boundary Value Problems, 2021
In this paper, we consider a class of Choquard equations with Hardy–Littlewood–Sobolev lower or upper critical exponent in the whole space R N $\mathbb{R}^{N}$ . We combine an argument of L. Jeanjean and H. Tanaka (see (Proc. Am. Math. Soc. 131:2399–2408,
Xiaowei Li, Feizhi Wang
doaj   +1 more source

Littlewood, Paley and almost‐orthogonality: a theory well ahead of its time

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract The classic paper by Littlewood and Paley [J. Lond. Math. Soc. (1), 6 (1931), 230–233] marked the birth of Littlewood–Paley theory. We discuss this paper and its impact from a historical perspective, include an outline of the results in the paper and their subsequent significance in relation to developments over the last century, and set them ...
Anthony Carbery
wiley   +1 more source

Riesz Potential on the Heisenberg Group

Journal of Inequalities and Applications, 2011
The relation between Riesz potential and heat kernel on the Heisenberg group is studied. Moreover, the Hardy-Littlewood-Sobolev inequality is established.
Xiao Jinsen, He Jianxun
doaj  

Some properties of solutions for a nonlinear integral system

Journal of Inequalities and Applications, 2016
In this paper, a nonlinear integral system is considered in critical space. Some important properties of positive solutions such as symmetry, monotonicity, integrability, and asymptotic behaviors, are obtained.
Xiaoying Wang, Junjie Li, Jiankai Xu
doaj   +1 more source

Existence of Solutions for Choquard Type Elliptic Problems with Doubly Critical Nonlinearities

Advanced Nonlinear Studies, 2021
In this article, we first study the existence of nontrivial solutions to the nonlocal elliptic problems in ℝN{\mathbb{R}^{N}} involving fractional Laplacians and the Hardy–Sobolev–Maz’ya potential.
Shen Yansheng
doaj   +1 more source

Function spaces for decoupling

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract We introduce new function spaces LW,sq,p(Rn)$\mathcal {L}_{W,s}^{q,p}(\mathbb {R}^{n})$ that yield a natural reformulation of the ℓqLp$\ell ^{q}L^{p}$ decoupling inequalities for the sphere and the light cone. These spaces are invariant under the Euclidean half‐wave propagators, but not under all Fourier integral operators unless p=q$p=q$, in ...
Andrew Hassell, Pierre Portal, Jan Rozendaal, Po‐Lam Yung   +3 more
wiley   +1 more source

Hardy–Littlewood–Sobolev inequalities on compact Riemannian manifolds and applications

Journal of Differential Equations, 2016
In this paper we extend Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds for dimension $n\ne 2$. As one application, we solve a generalized Yamabe problem on locally conforamlly flat manifolds via a new designed energy functional and a new variational approach.
Yazhou Han, Meijun Zhu
openaire   +2 more sources

Hardy inequality: genesis and applications [PDF]

, 2022
openArgomento principale della tesi è la disuguaglianza di Hardy. Dopo averla introdotta nella sua forma sia discreta che continua, dimostrata e averne dato qualche generalizzazione, introdurremo la nozione di spazio di Sobolev, illustrando le ...
TEDESCO, NICOLÒ
core  

On a critical Choquard-Kirchhoff p-sub-Laplacian equation in ℍn

Analysis and Geometry in Metric Spaces
This article is devoted to the study of a critical Choquard-Kirchhoff pp-sub-Laplacian equation on the entire Heisenberg group Hn{{\mathbb{H}}}^{n}, where the Kirchhoff function KK can be zero at zero, i.e., the equation can be degenerate, and involving ...
Liang Sihua, Pucci Patrizia, Song Yueqiang, Sun Xueqi   +3 more
doaj   +1 more source