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 … WebSep 1, 2016 · Hardy–Littlewood–Sobolev theorem of G-Riesz potential on L p, ... G-Riesz potential. G-maximal function. G-BMO space. 0. Introduction. The Hardy–Littlewood maximal function is an important tool of harmonic analysis. It was first introduced by Hardy and Littlewood in 1930 (see ) ...
integration - Fractional integral inequality (Hardy-Littlewood ...
WebMar 6, 2024 · Hardy–Littlewood–Sobolev lemma. Sobolev's original proof of the Sobolev embedding theorem relied on the following, sometimes known as the … WebJun 13, 2024 · Hardy-Littlewood inequality is a special case of Young's inequality. Young's inequality has been extended to Lorentz spaces in this paper O'Neil, R. O’Neil, Convolution operators and L ( p, q) spaces, Duke Math. J. 30 (1963), 129–142. Unfortunately, you need a subscription to access the paper. pinnacle state park california
Hardy-Littlewood-Sobolev Theorems of Fractional Integration on …
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 … WebOct 11, 2024 · In other words, the Har dy–Littlewood–Sobolev inequality fails at p = 1 (see Chapter 5 in [33] for the original Har dy–Littlewood–Sobolev inequality and its applications). Definition 1.5. WebApr 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. steinhauer automotive junction city oregon