Sentence examples for maximal functions and from inspiring English sources

In Section 2, we recall some important estimates on BMO functions, maximal functions and sharp maximal functions.

In Section 2, we will recall some basic facts concerning weights, maximal functions, sharp maximal functions and characterization of the space (dot{wedge}_{beta }).

A measure of noncompactness (essential norm) for maximal functions and potential operators defined on homogeneous groups is estimated in terms of weights.

In 2009, the authors [7] introduced the new multiple weights and new maximal functions and obtained some weighted estimates for multilinear Calderón-Zygmund singular integrals.

We establish well-posedness of the Dirichlet problem for the equation Lu= 0, with boundary data in L2, and with optimal estimates in terms of nontangential maximal functions and square functions.

In particular, the proof of Theorem B is highly dependent on a summability argument over the sequence of local maximal and local minima of discrete multisublinear fractional maximal functions and two summability estimates (see [33, Lemmas 2.1 2.2]).

We begin by introducing a class of multilinear maximal function and multilinear fractional integral operators.

In this paper, we introduce the sharp maximal function in this general setting, and establish the equivalence of theLpnorms between the sharp maximal function and the Hardy Littlewood maximal function, as well the John Nirenberg type inequalities.

Theorem 1.2 can be regarded as cross-weighted norm inequalities for the Hardy-Littlewood maximal function and the sharp maximal function on the unit sphere.

In particular, the maximal function and sharp function theorems on bounded domains we use in this paper require such information.

In this article, the authors first introduce the variable weak Hardy space on Rn, WHp(Rn), via the radial grand maximal function, and then establish its radial or non-tangential maximal function characterizations.