Let dγ(x) ≡ πe 2 dx for all x ∈ R be the Gauss measure on R. In this paper, the authors establish the characterizations of the space BMO(γ) of Mauceri and Meda via commutators of either local fractional integral operators or local fractional maximal operators. To this end, the authors first prove that such a local fractional integral operator of order β is bounded from L(γ) to L(γ), or from the...

It la well-known thaI if u E W”’(12), (2 cE .~t satisfles On E L~(fl), then u belonga te BMO(9), Ihe John-Nirenberg Space. Wc prove that Ihis ja no more true if ¡ Dii belonga te an Orlicz apace LÁ((2) whcn the N-function AQ) increases leas Ihan it. In arder te obtain u E BMO ((2), we impose a suitable uniform LA conditien for Dii

{ / E L (Q) : ]Q O, "'"BMO(O) sup (~"~1~-~1 ]2)1/9-} = = = < : (X ~ , BEA(o") while VM0(Q) is the dyadic space dual to H We define the '~aorm" of the bijection .T: A (2)-+ A (2) as follows: Iljrll~= sup ([Urlc-Bjr(II)[.) 1/2 T h e o r e m 1. Suppose that jr: A (2)-+ A (2) /s an arbitrary bijection, jr(Q) = Q. Then lIRa)-, IIBMo(Q)-~BMO(Q) > II-rl12

This paper is devoted to the decomposition of an image f into u + v, with u a piecewise-smooth or “cartoon” component, and v an oscillatory component (texture or noise), in a variational approach. The cartoon component u is modeled by a function of bounded variation, while v, usually represented by a square integrable function, is now being modeled by a more refined and weaker texture norm, as ...

We prove that the multiparameter (product) space BMO of functions of bounded mean oscillation can be written as the intersection of finitely many dyadic product BMO spaces, with equivalent norms, generalizing the one-parameter result of T. Mei. We establish the analogous dyadic structure theorems for the space VMO of functions of vanishing mean oscillation, for Ap weights, for reverse-Hölder we...

Peetre's A"-functional for the Hardy space Hp, 0 < p < +00, and the space BMO of functions of bounded mean oscillation is explicitly characterized in the case of a product of upper half-spaces.

Purpose To identify determinants of Bruch's membrane opening (BMO), and BMO-minimum rim width (BMO-MRW) and circumpapillary retinal nerve fiber layer thickness (RNFLT) centered on BMO center and characterize these parameters in a normal Japanese population. Methods Spectral-domain optical coherence tomography images of optic nerve head and circumpapillary and macular retina were obtained in 2...

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...

A precise evaluation of the retinal nerve fiber layer thickness (RNFLT) is key for diagnosing and monitoring glaucoma. The Bruch's membrane opening minimum rim width (BMO-MRW) has been proposed as a reproducible assessment of the optic nerve. The BMO-MRW measures the minimum distance from the BMO to the internal limiting membrane. We propose an approach to correct the BMO-MRW using the BMO size...

In this paper, we prove that the weighted BMO space $${\rm{BM}}{{\rm{O}}^p}(\omega ) = \left\{ {f \in L_{{\rm{loc}}}^1:\mathop {\sup }\limits_Q \left\| {{\chi _Q}} \right\|_{{L^p}(\omega )}^{ - 1}{{\left\| {(f {f_Q}){\omega ^{ 1}}{\chi \right\|}_{{L^p}(\omega )}} < \infty } \right\}$$ is independent of scale p ∈ (0, ∞) in sense norm when ω A1. Moreover, can replace Lp(ω) by Lp,∞(ω). As an appli...