H ·H := ̆ h = fg : f, g ∈ H ̄ = H ←↩ H is the product space of H2, by inner/outer factorization and Cauchy-Schwarz inequality. It is interesting, then, to find the dual space of H1. C. Fefferman [7] proved that, under the H2 paring (with some care), (H2 ·H2)∗ = (H1)∗ = BMO∩H(D) is the space of the analytic functions with bounded mean oscillation. The definition of BMO, born out of a problem in el...

Recently, using DiGiorgi-type techniques, Caffarelli and Vasseur [1] showed that a certain class of weak solutions to the drift diffusion equation with initial data in L gain Hölder continuity provided that the BMO norm of the drift velocity is bounded uniformly in time. We show a related result: a uniform bound on BMO norm of a smooth velocity implies uniform bound on the C norm of the solutio...

We establish a connection between the function space BMO and theory of quasisymmetric mappings on \emph{spaces homogeneous type} $\widetilde{X} :=(X,\rho,\mu)$. The is that logarithm generalised Jacobian an $\eta$-quasisymmetric mapping $f: \widetilde{X} \rightarrow \widetilde{X}$ always in $\rm{BMO}(\widetilde{X})$. In course proving this result, we first show $\widetilde{X}$, reverse-H\"{o}ld...

The main part of this note is to show a general covering lemma in Rn, n 2 2 , with the aim to obtain the estimate for BMO norm and the volume of a nodal set of eigenfunctions on Riemannian manifolds. This article is a continuation of our previous work [L]. In [L] we proved a covering lemma in R2 and applied it to the BMO norm estimates for eigenfunctions on Riemannian surfaces. The principal pa...

INTRODUCTION The goal of this retrospective study was to evaluate the safety and efficacy of ibandronate for bone marrow oedema (BMO) syndrome and stress fracture cases, and to demonstrate an additional field of therapeutic importance-the high-performance athlete. PATIENTS AND METHODS This retrospective study included twenty-five high-performance athletes. Sixty per cent of the athletes were ...

We prove that the Bloch space coincides with the space BMOA in the tube over the spherical cone of R.3; this extends a well-known onedimensional result. Introduction. Let Q be a symmetric Siegel domain of type II contained in Cn. Let V denote the Lebesgue measure in fi and H{Q) the space of holomorphic (or analytic) functions in fi. When n = 1 and fi = tt+ = {z £ C: Imz > 0}, a Bloch function i...

PURPOSE Lamina cribrosa (LC) morphology could be implicated in the progression of glaucoma. To date, no established, quantifiable parameter to assess LC shape in vivo exists. We aim to introduce a new global shape index for the anterior LC (LC-GSI) and to identify associations with ocular factors in a healthy Indian population. METHODS Optical coherence tomography (OCT) scans of the optic ner...

Butane monooxygenase (BMO) from Pseudomonas butanovora has high homology to soluble methane monooxygenase (sMMO), and both oxidize a wide range of hydrocarbons; yet previous studies have not demonstrated methane oxidation by BMO. Studies to understand the basis for this difference were initiated by making single-amino-acid substitutions in the hydroxylase alpha subunit of butane monooxygenase (...