WebNov 3, 2016 · Inequalities. By G.H. Hardy, J.E. Littlewood and G. Pólya. 2nd edition. Pp. xii, 324. 27s. 6d. 1952. (Cambridge University Press) - Volume 37 Issue 321 WebMay 20, 2024 · Finally, by using the method of moving plane in integral forms, we prove that extremals of the Hardy-Littlewood-Sobolev inequality with the fractional Poisson kernel must be radially symmetric and decreasing about some point \({\xi _0}\, \in \,\partial \mathbb{R}_+ ^n.\)
Sharp Estimates of m-Linear p-Adic Hardy and Hardy-Littlewood …
WebSuch inequalities are the continuous versions of the classical rearrangement inequalities for discrete sets of numbers. I am interested in the equality case in (HL). As far as the rightmost inequality is concerned, there is a vast literature on the subject. WebIn this paper, first we present some interesting identities associated with Green’s functions and Fink’s identity, and further we present some interesting inequalities for r-convex … mossy oaks south carolina
real analysis - Hardy-Littlewood-Sobolev inequality using …
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. In mathematical analysis, the Hardy–Littlewood inequality, named after G. H. Hardy and John Edensor Littlewood, states that if $${\displaystyle f}$$ and $${\displaystyle g}$$ are nonnegative measurable real functions vanishing at infinity that are defined on $${\displaystyle n}$$-dimensional … See more The layer cake representation allows us to write the general functions $${\displaystyle f}$$ and $${\displaystyle g}$$ in the form $${\displaystyle f(x)=\int _{0}^{\infty }\chi _{f(x)>r}\,dr\quad }$$ and where See more • Rearrangement inequality • Chebyshev's sum inequality • Lorentz space See more Web ∫ℝn∫ℝnf(x) x−y −λg(y)𝑑x𝑑y ≥N(n,λ,p)‖f‖Lp(ℝn)‖g‖Lt(ℝn ... mossy oaks realty indiana