Sentence examples for maximal function and from inspiring English sources

Topics include Lebesgue measure on Euclidean space, Lebesgue integration, L^p spaces, the Fourier transform, the Hardy-Littlewood maximal function and Lebesgue differentiation.

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

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 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.

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.

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

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.

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 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).

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 }).