WebSep 15, 2014 · E. Carlen, J.A. Carrillo and M. Loss noticed in [12] that Hardy–Littlewood–Sobolev inequalities in dimension d ≥ 3 can be deduced from some … 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
SOBOLEV AND HARDY-LITTLEWOOD-SOBOLEV …
WebMikhail Borsuk, Vladimir Kondratiev, in North-Holland Mathematical Library, 2006. 2.7 Notes. The classical Hardy inequality was first proved by G. Hardy [142].The various extensions of this inequality as well the proof of Theorem 2.8 can be found in [362, 108].For other versions of the Poincaré inequality, see §2.22 [108]. The one-dimensional Wirtinger … leatherwood scent
Hardy-Littlewood-Sobolev inequalities via fast diffusion flows
Web本书专门介绍（带π的那个）Carlson不等式相关研究，正好与前面Hilbert不等式，Hardy不等式这类带奇妙常数的不等式书籍呈鼎足之势。 本书先讲证明，再给出一些基础重要的推广，再讨论多维的，加权的推广，继而从Interpolation的角度抽象概括了这一类不等式。 WebMar 24, 2024 · References Broadbent, T. A. A. "A Proof of Hardy's Convergence Theorem." J. London Math. Soc. 3, 232-243, 1928.Elliot, E. B. "A Simple Exposition of Some … This theorem of G. H. Hardy and J. E. Littlewood states that M is bounded as a sublinear operator from the L (R ) to itself for p > 1. That is, if f ∈ L (R ) then the maximal function Mf is weak L -bounded and Mf ∈ L (R ). Before stating the theorem more precisely, for simplicity, let {f > t} denote the set {x f(x) > t}. Now we have: Theorem (Weak Type Estimate). For d ≥ 1, there is a constant Cd > 0 such that for all λ > 0 an… leatherwood rosin bass