WebMar 30, 2024 · Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their … In their original paper, G.H. Hardy and J.E. Littlewood explained their maximal inequality in the language of cricket averages. Given a function f defined on R , the uncentred Hardy–Littlewood maximal function Mf of f is defined as at each x in R . Here, the supremum is taken over balls B in R which contain the point x and B denotes the measure of B (in this case a multiple of the radius of the ball raised to the power n). …
The Hardy-Littlewood maximal inequality (discrete version)
Web2 HARDY-LITTLEWOOD-SOBOLEV INEQUALITY Is it sharp? It seems to be 2n instead of 6n, but I’m not sure and at least hard to prove. This coefficient is not so important for the proof be given later, so let’s go over it. 2. Hardy-Littlewood maximal function Denote the average of f on A by H A f := 1 VolA R A f. The Hardy-Littlewood maximal WebThe Hardy-Littlewood maximal function and its generalizations, because of their tight relation with so-called singular integrals (operators that can be realized as a convolution … il mondo berlin rathausstraße
Hardy-Littlewood maximal function - MathOverflow
WebMaximal Functions in Sobolev Spaces. Part of the International Mathematical Series book series (IMAT,volume 8) Applications of the Hardy—Littlewood maximal functions in the modern theory of partial differential equations are considered. In particular, we discuss the behavior of maximal functions in Sobolev spaces, Hardy inequalities, and ... WebDec 11, 2012 · On the Hardy-Littlewood maximal function for the cube. Jean Bourgain. It is shown that the Hardy-Littlewood maximal function associated to the cube in \mathbb R^n obeys dimensional free bounds in L^p fir p>1. Earlier work only covered the range p>\frac 32 . Comments: WebA will not occur again in the sense of Section III. Constants B, C in future presserve their identity. Sn (θ) is formed from the first n +1 terms of the Fourier series of f (θ), σ n (θ) from the first n. When θ 1/2π by r =0. The usefulness of a kernel of the type of X was first pointed out ... il mondo by il volo youtube