WebApr 23, 2024 · The Hardy-Littlewood-Sobolev inequality is the statement that there is a C > 0 such that ‖f ∗ ⋅ − α‖p ≤ C‖f‖q, for all f ∈ Lq(Rd), where the convolution is defined as (f ∗ … 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 …
Sobolev inequality - Wikipedia
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. 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 … the beacon hospital beckenham
integration - Fractional integral inequality (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. 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.. The decreasing … WebSamuel B. Hardy (March 21, 1883 – October 16, 1935) was an American stage and film actor who appeared in feature films during the silent and early sound eras.. Born in New … the health benefits of basil