Sentence examples for sharp function from inspiring English sources

In [20], a sharp function estimate of the strongly singular integral operator is obtained.

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

Based on this, one can use the standard real analysis tools as the maximal function Mf and the sharp function (M^{sharp}f).

Since the sharp function for the classical Hardy operator does not exist, it is easy to know from inequality (12) that there exists no function f such that (mathcal{R}_{mu}(f)=frac{p}{p-1}).

Finally, in order to deal with the system (1.2) in a Lipschitz domain, we apply a version of the Fefferman Stein sharp function theorem for spaces of homogeneous type, which was recently proved in [12] (cf. Lemma 7.3).

The main purpose of this paper is to prove a sharp function inequality for the multilinear singular integral operator with non-smooth kernel when D α b j ∈ BMO ( R n ) for all α with | α | = m j.

These studies all add to the accumulating evidence that says that exercise is good for everyone (Ploughman 2008), irrespective of age and may also keep our brains in sharper function by stimulating and maintaining neurogenesis.

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

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

The proofs of Theorems 1.1 and 1.2 will be given in Section 2. We start Section 2 by introducing the sharp maximal function and a lemma on the sharp maximal function, which plays an important role in the proof of the main theorem.

This paper is to establish the weighted norm inequality for commutators of Calderón-Zygmund operators with functions by an estimate for a variant of the sharp maximal function in the context of the nonhomogeneous spaces.