WebApr 23, 2024 · Remark 1.The inequality (n-HLS) actually holds for $\frac1 p - \frac1q +1 \le \frac{\alpha}{d}$.However, the non-endpoint case $\frac1 p - \frac1q +1 < … 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
The Hardy-Littlewood maximal inequality - UCLA …
WebThis is a corollary of the Hardy–Littlewood maximal inequality. Hardy–Littlewood maximal inequality. This theorem of G. H. Hardy and J. E. Littlewood states that M is bounded as a sublinear operator from the L p (R d) to itself for p > 1. That is, if f ∈ L p (R d) then the maximal function Mf is weak L 1-bounded and Mf ∈ L p (R d). WebAug 16, 2001 · Hardy-Littlewood maximal inequality By Antonios D. Melas Abstract We find the exact value of the best possible constant C for the weak-type ... The simplest example of such a maximal operator is the centered Hardy-Littlewood maximal operator defined by (1.1) Mf(x)=sup h>0 1 2h x+h x−h f for every f ∈ L1(R ). ceu stroke education
Hardy—Littlewood—Sobolev Inequalities with the Fractional …
WebHardy-Littlewood-Po´lya inequality are also included. 1. Introduction The Hardy-Littlewood-Po´lya theorem of majorization is an important result in convex analysis that … WebDiscrete HardyLittlewood 2 and the associated function ma (c) = Ma). This is also the onedimensional measure of the intersection of the line y = c and the region {(x,y) 0 ≤ y ≤ … 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. ceus union city nj