nontangential maximal function
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2011 ◽  
Vol 09 (03) ◽  
pp. 345-368 ◽  
Author(s):  
DACHUN YANG ◽  
DONGYONG YANG

Let λ > 0, p ∈ ((2λ + 1)/(2λ + 2), 1], and [Formula: see text] be the Bessel operator. In this paper, the authors establish the characterizations of atomic Hardy spaces Hp((0,∞),dmλ) associated with △λ in terms of the radial maximal function, the nontangential maximal function, the grand maximal function, the Littlewood–Paley g-function and the Lusin-area function, where dmλ(x) ≡ x2λ dx. As an application, the authors further obtain the Riesz transform characterization of these Hardy spaces.


2007 ◽  
Vol 2007 ◽  
pp. 1-13
Author(s):  
Jorge Rivera-Noriega

We prove distributional inequalities that imply the comparability of theLpnorms of the multiplicative square function ofuand the nontangential maximal function oflogu, whereuis a positive solution of a nondivergence elliptic equation. We also give criteria for singularity and mutual absolute continuity with respect to harmonic measure of any Borel measure defined on a Lipschitz domain based on these distributional inequalities. This extends recent work of M. González and A. Nicolau where the term multiplicative square functions is introduced and where the case whenuis a harmonic function is considered.


2004 ◽  
Vol 56 (3) ◽  
pp. 655-672 ◽  
Author(s):  
Xiangxing Tao ◽  
Henggeng Wang

AbstractWe consider the Neumann problem for the Schrödinger equations –Δu + Vu = 0, with singular nonnegative potentials V belonging to the reverse Hölder class ℬn, in a connected Lipschitz domain Ω Rn. Given boundary data g in Hp or Lp for 1 – ɛ < p ≤ 2, where 0 < ɛ < , it is shown that there is a unique solution, u, that solves the Neumann problem for the given data and such that the nontangential maximal function of ▽u is in Lp(∂Ω). Moreover, the uniform estimates are found.


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