We study tent spaces on general measure spaces (Ω, μ). We assume that there exists a semigroup of positive operators on Lp(Ω, μ) satisfying a monotone property but do not assume any geometric/metric structure on Ω. The semigroup plays the same role as integrals on cones and cubes in Euclidean spaces. We then study BMO spaces on general measure spaces and get an analogue of Fefferman’s H1-BMO du...

The seminal paper of Coifman et al. (1993) has triggered numerous new applications of Hardy spaces and the space BMO of functions of bounded mean oscillation to nonlinear partial differential equations. These applications include various problems of variational and geometric origin: harmonic and p-harmonic maps, H-systems, wave maps; (see, e.g., Bethuel, 1993; Evans, 1991; Hélein, 1998, 2002; T...

Weighted L for p ∈ 1,∞ and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. Al...

We establish a connection between the absolute continuity of elliptic measure associated to a second order divergence form operator with bounded measurable coefficients with the solvability of an endpoint BMO Dirichlet problem. We show that these two notions are equivalent. As a consequence we obtain an end-point perturbation result, i.e., the solvability of the BMO Dirichlet problem implies Lp...

PURPOSE To observe the relationship between topographic hemoglobin levels in the optic nerve head (ONH), the rim thickness (BMO-MRW), and retinal nerve fiber layer (RNFL) thickness. METHODS 96 normal eyes and 82 glaucomas were examined using TOP strategy (Octopus 300 perimeter), SPECTRALIS OCT, and Laguna ONhE program which estimates hemoglobin from conventional color photographs (Horus Scope...

PURPOSE To describe longitudinal rates of change of neuroretinal parameters in patients with glaucoma and healthy controls, and to evaluate the influence of covariates. DESIGN Prospective longitudinal study. PARTICIPANTS Treated patients with glaucoma (n = 192) and healthy controls (n = 37). METHODS Global disc margin-based neuroretinal rim area (DMRA) was measured with confocal scanning ...

Let f be a Borel measurable function of the complex plane to itself. We consider the nonlinear operator Tf defined by Tf [g] = f ◦ g, when g belongs to a certain subspace X of the space BMO(Rn) of functions with bounded mean oscillation on the Euclidean space. In particular, we investigate the case in which X is the whole of BMO, the case in which X is the space VMO of functions with vanishing ...

Let L = −∆+ V be a Schrödinger operator on R, d ≥ 3, where V is a nonnegative function, V 6= 0, and belongs to the reverse Hölder class RHd/2. The purpose of this paper is three-fold. First, we prove a version of the classical theorem of Jones and Journé on weak∗-convergence in H L(R ). Secondly, we give a bilinear decomposition for the product space H L(R )×BMOL(R). Finally, we study the commu...

In this paper, we show a parabolic version of the Ogawa type inequality in Sobolev spaces. Our inequality provides an estimate of the L∞ norm of a function in terms of its parabolic BMO norm, with the aid of the square root of the logarithmic dependency of a higher order Sobolev norm. The proof is mainly based on the Littlewood-Paley decomposition and a characterization of parabolic BMO spaces....

Purpose To compare optic nerve head (ONH) measurements in glaucomatous eyes with paracentral visual field (VF) loss to eyes with peripheral VF loss and controls. Methods Open-angle glaucoma (OAG) patients with early paracentral VF loss or isolated peripheral VF loss as well as control subjects underwent ONH imaging with swept-source optical coherence tomography (OCT) and retinal nerve fiber l...