Sentence examples for by maximal function and from inspiring English sources

In the case 0 < p ⩽ 1 we find the UMD property as the necessary and sufficient condition to make the spaces defined by maximal function and by conjugate Poisson kernel coincide.

In the present paper we define Hardy spaces with variable exponents on Rn by the grand maximal function, and then investigate their several properties.

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.

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

And then by adding a suitable regularity condition on a weight function, we derive and prove a cross-weighted norm inequalities between the Hardy-Littlewood maximal function and the sharp maximal function.

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.

Following the Hedberg trick [23], we plan to control I 1 by J ε f ( x ) not by maximal functions (Lemma 2.3).

In this paper, the authors first show that the classical Hardy space H1(Rn) can be characterized by the non-tangential maximal functions and the area integrals associated with the semigroups e−tP and e−t√P, respectively, where P is an elliptic operator with real constant coefficients of homogeneous order 2m (m⩾1).

The paper concludes with the Lp Lq boundedness and the boundedness on weighted Morrey spaces of the associated Riesz potential Iδλf, by means of two different fractional maximal functions, and also the Hpλ(D Hqλ(D) boundedness of Iδλf for p0

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