The Best Constant for the Centered Maximal Operator on Radial Functions
نویسنده
چکیده
We show that the lowest constant appearing in the weak type (1,1) inequality satisfied by the centered Hardy-Littlewood maximal operator on radial integrable functions is 1.
منابع مشابه
On the Lp boundedness of the non-centered Gaussian Hardy-Littlewood Maximal Function
The purpose of this paper is to prove the L p (R n ; dd) boundedness, for p > 1, of the non-centered Hardy-Littlewood maximal operator associated with the Gaussian measure dd = e ?jxj 2 dx. Let dd = e ?jxj 2 dx be a Gaussian measure in Euclidean space R n. We consider the non-centered maximal function deened by Mf(x) = sup x2B 1 (B) Z B jfj dd; where the supremum is taken over all balls B in R ...
متن کاملDimension Dependency of the Weak Type (1, 1) Bounds for Maximal Functions Associated to Finite Radial Measures
We show that the best constants appearing in the weak type (1,1) inequalities satisfied by the centered Hardy-Littlewood maximal function associated to some finite radial measures, such as the standard gaussian measure, grow exponentially fast with the dimension.
متن کامل$L_k$-biharmonic spacelike hypersurfaces in Minkowski $4$-space $mathbb{E}_1^4$
Biharmonic surfaces in Euclidean space $mathbb{E}^3$ are firstly studied from a differential geometric point of view by Bang-Yen Chen, who showed that the only biharmonic surfaces are minimal ones. A surface $x : M^2rightarrowmathbb{E}^{3}$ is called biharmonic if $Delta^2x=0$, where $Delta$ is the Laplace operator of $M^2$. We study the $L_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...
متن کاملThe Universal Maximal Operator on Special Classes of Functions
We prove pointwise inequalities for the maximal operator over all the directions in R when acting on l-radial functions and on product functions. From these inequalities we deduce boundedness results on L for p > n; these can be applied to other operators, in particular to the Kakeya maximal operator.
متن کاملMQ-Radial Basis Functions Center Nodes Selection with PROMETHEE Technique
In this paper, we decide to select the best center nodes of radial basis functions by applying the Multiple Criteria Decision Making (MCDM) techniques. Two methods based on radial basis functions to approximate the solution of partial differential equation by using collocation method are applied. The first is based on the Kansa's approach, and the second is based on the Hermit...
متن کامل