The solvability in Sobolev spaces is proved for divergence form second order elliptic equations in the whole space, a half space, and a bounded Lipschitz domain. For equations in the whole space or a half space, the leading coefficients a are assumed to be measurable in one direction and have small BMO semi-norms in the other directions. For equations in a bounded domain, additionally we assume...

We prove that the weak Morrey space WM is contained in $$M_{{q_1}}^p$$ for 1 ≤ q1 < q p ∞. As applications, we show if commutator [b, T] bounded from Lp to Lp,∞ some ∈ (1, ∞), then b BMO, where T a Calderón-Zygmund operator. Also, ∞, BMO and only [6, M . For belonging Lipschitz class, obtain similar results.

PURPOSE We determined if the Bruch's membrane opening (BMO) location changes over time in healthy eyes and eyes with progressing glaucoma, and validated an automated segmentation algorithm for identifying the BMO in Cirrus high-definition coherence tomography (HD-OCT) images. METHODS We followed 95 eyes (35 progressing glaucoma and 60 healthy) for an average of 3.7 ± 1.1 years. A stable group...

the aim of this paper is a) if σak2 < ∞ then σak rk(x) is in bmo that{rk(x)} is rademacher system. b) p1k=1 ak!nk (x) 2 bmo; 2k  nk < 2k+1that f!n(x)g is walsh system. c) if jakj < 1k then p1k=1 ak!k(x) 2 bmo.

In order to extend the blow-up criterion of solutions to the Euler equations, Kozono and Taniuchi [12] have proved a logarithmic Sobolev inequality by means of isotropic (elliptic) BMO norm. In this paper, we show a parabolic version of the Kozono-Taniuchi inequality by means of anisotropic (parabolic) BMO norm. More precisely we give an upper bound for the L∞ norm of a function in terms of its...

Purpose To test the hypotheses that: (1) structure-function (SF) relationships between visual fields (VF) and Bruch's membrane opening-based minimum rim width (BMO-MRW) measurements are superior to those for peripapillary retinal nerve fiber layer (pRNFL) in perimetric glaucoma; (2) BMO-MRW measurements may extend the utility of structural measurement across the range of glaucoma severity; and ...

X. Tolsa defined the space of type BMO for a positive Radon measure satisfying some growth condition on R. This space is very suitable for the CalderónZygmund theory with non-doubling measures. Especially, the John-Nirenberg type inequality remains true. In this paper we introduce the localized and weighted version of this inequality and, as an application, we obtain some vector-valued inequali...

The main purpose of this paper is two-fold. On one hand, we prove a sharper covering lemma in Euclidean space Rn for all n ≥ 2 (see Theorem 1.5). On the other hand, we apply this covering lemma to improve existing results for BMO and volume estimates of nodal sets for eigenfunctions u satisfying 4u + λu = 0 on n-dimensional Riemannian manifolds when λ is large (see Theorems 1.7, 1.8). We also i...

Our previous short-term experiment demonstrated that seed oil from bitter melon (Momordica charantia) (BMO), which is rich in cis(c)9, trans(t)11, t13-conjugated linolenic acid (CLN), inhibited the development of azoxymethane (AOM)induced colonic aberrant crypt foci (ACF). In our study, the possible inhibitory effect of dietary administration of BMO on the development of colonic neoplasms was i...