Let b be aBMO-function. It is well-known that the linear commutator [b, T ] of a Calderón-Zygmund operator T does not, in general, map continuously H(R) into L(R). However, Pérez showed that if H(R) is replaced by a suitable atomic subspace H b(R ) then the commutator is continuous from H b(R ) into L(R). In this paper, we find the largest subspace H b (R ) such that all commutators of Calderón...

BACKGROUND For cervical carcinoma cases, this study aimed to evaluate the quality of intensity-modulated radiation therapy (IMRT) plans optimized by biological constraints. Furthermore, a new integrated strategy in biological planning module was proposed and verified. METHODS Twenty patients of advanced stage cervical carcinoma were enrolled in this study. For each patient, dose volume optimi...

PURPOSE This study explores variation in the axial location of Bruch's membrane opening (BMO) to determine if this reference plane varies with age and race. METHODS There were 168 spectral-domain optical coherence tomography (SDOCT) optic nerve head volumes that were obtained from healthy subjects and manually delineated within 24 axial slices to develop point clouds for Bruch's membrane and ...

PURPOSE This study examined the association between peripapillary choroidal thickness (PCT) with age and race in a group of African descent (AD) and European descent (ED) subjects with normal eyes. METHODS Optic nerve head images from enhanced depth imaging spectral-domain optical coherence tomography of 166 normal eyes from 84 subjects of AD and ED were manually delineated to identify the pr...

1. Introduction. The Calderón-Zygmund theory of singular integrals has been traditionally considered with respect to a measure satisfying a doubling condition. Recently, Tolsa [T] and, independently, Nazarov, Treil, and Volberg [NTV] have shown that this standard doubling condition was not really necessary. Likewise, in the homogeneous spaces setting, functions of bounded mean oscillation, BMO,...

The functions with bounded mean oscillation (BMO) have been shown to be immense interest in several areas of analysis and probability. We introduce BMO-type space BMOHK(Rn) for non-absolute integrable functions. Various properties completion are included. Relations between the classical BMO investigated.

We address $L^p(\mu)\to L^p(\lambda)$ bounds for paraproducts in the Bloom setting. introduce certain “sparse BMO” functions associated with sparse collections no infinitely increasing chains, and use these to express operators as sums of martingale transforms – essentially, Haar multipliers well obtain an equivalence norms between $\mathcal{A}\_{\mathcal{S}}$ compositions $\Pi^\*\_a\Pi\_b$.

Let 0 < q < ∞ and Lqloc(R n) = {f q is locally integrable on Rn}. Suppose f ∈ Lloc(R), B = B(x0, r) = {x ∈ Rn : |x − x0| < r} denotes a ball of Rn centered at x0 and having radius r, write fB = |B|−1 ∫ B f(x)dx and f #(x) = supx∈B |B|−1 ∫ B |f(x) − fB|dx < ∞. f is said to belong to BMO(R n), if f# ∈ L∞(Rn) and define ||f ||BMO = ||f||L∞ . Let T be the Calderón-Zygmund singular integral operator...

Consider the second order divergence form elliptic operator L with complex bounded coefficients. In general, the operators related to it (such as Riesz transform or square function) lie beyond the scope of the Calderón-Zygmund theory. They need not be bounded in the classical Hardy, BMO and even some Lp spaces. In this work we generalize the classical approach and develop a theory of Hardy and ...

Consider a second order divergence form elliptic operator L with complex bounded coefficients. In general, operators related to it (such as the Riesz transform or square function) lie beyond the scope of the Calderón-Zygmund theory. They need not be bounded in the classical Hardy, BMO and even some Lp spaces. In this work we develop a theory of Hardy and BMO spaces associated to L, which includ...