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Functions of Vanishing Mean Oscillation [PDF]
Transactions of the American Mathematical Society, 1975 A function of bounded mean oscillation is said to have vanishing mean oscillation if, roughly speaking, its mean oscillation is locally small, in a uniform sense. In the present paper the class of functions of vanishing mean oscillation is characterized in several ways. This class is then applied to answer two questions in analysis,
Donald Sarason, Sarason Donald
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Bounded functions of vanishing mean oscillation on compact metric spaces [PDF]
Journal of Functional Analysis, 2004 Consider a metric space \((X,\,\rho)\) with a doubling measure \(\mu\). Generalizing a classical result due to \textit{T. H. Wolff} [Duke Math. J. 49, 321--328 (1982; Zbl 0494.30042)], the author proves that for every \(f\in L^{\infty}(\mu)\) there exists \(\eta\in VMO(X,d,\mu)\) such that \(0\leq\eta\leq 1\), \(\log\eta\in VMO(X,d,\mu)\), and \(\eta f\
Jingbo Xia
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Extension theorems for functions of vanishing mean oscillation [PDF]
Pacific Journal of Mathematics, 1990 A locally integrable function is said to be of vanishing mean oscillation (VMO) if its mean oscillation over cubes in Rd converges to zero with the volume of the cubes. We establish necessary and sufficient conditions for a locally integrable function defined on a bounded measurable set of positive measure to be the restriction to that set of a VMO ...
Peter Holden
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Functions of vanishing mean oscillation associated with operators and applications [PDF]
Michigan Mathematical Journal, 2008 The authors introduce new function spaces \(\mathbf{VMO}_L (\mathbb{R}^n)\) of vanishing mean oscillation associated with infinitesimal generators of analytic semigroups on \(L^2 (\mathbb{R}^n)\). Such spaces generalize the classical \(\mathbf{VMO}\) space. Let \(L^*\) denote the adjoint of the operator \(L\). The main result of the paper is that under
Xuan Thinh Duong +2 more
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Holomorphic semigroups and Sarason’s characterization of vanishing mean oscillation [PDF]
Revista Matemática Iberoamericana, 2022 It is a classical theorem of Sarason that an analytic function of bounded mean oscillation (BMOA) is of vanishing mean oscillation if and only if its rotations converge in norm to the original function as the angle of the rotation tends to zero. In a series of two papers, Blasco et al.
Chalmoukis, Nikolaos +1 more
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Seasonal and El Niño–Southern Oscillation-related ocean variability in the Panama Bight [PDF]
Ocean Science, 2023 In the Panama Bight, two different seasonal surface circulation patterns coincide with a strong mean sea level variation, as observed from 27 years of absolute dynamic topography (ADT) and the use of self-organizing maps.
R. R. Torres +5 more
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Vanishing mean oscillation and continuity of rearrangements
Advances in MathematicsWe study the decreasing rearrangement of functions in VMO, and show that for rearrangeable functions, the mapping f -> f* preserves vanishing mean oscillation. Moreover, as a map on BMO, while bounded, it is not continuous, but continuity holds at points in VMO (under certain conditions).
Almut Burchard +2 more
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Local vanishing mean oscillation
Bulletin De La Societe Mathematique De FranceWe consider various notions of vanishing mean oscillation on a (possibly unbounded) domain $Ω\subset \mathbb{R}^n$, and prove an analogue of Sarason's theorem, giving sufficient conditions for the density of bounded Lipschitz functions in the nonhomogeneous space $\rm{vmo}(Ω)$. We also study $\rm{cmo}(Ω)$, the closure in $\rm{bmo}(Ω)$ of the continuous
Butaev, Almaz, Dafni, Galia
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Functions of vanishing mean oscillation associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates [PDF]
Tohoku Mathematical Journal, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Extreme points in spaces between Dirichlet and Vanishing Mean Oscillation [PDF]
Bulletin of the Australian Mathematical Society, 2003 Forp∈ (0, ∞) defineQp0(∂Δ) as the space of all Lebesgue measurable complex-valued functionsf; on the unit circle ∂Δ for which ∫∂Δf;(z)|dz|/(2π) = 0 andas the open subarcIof ∂Δ varies. Note that eachQp,0(∂Δ) lies between the Dirichlet space and Sarason's vanishing mean oscillation space.
Wirths, K. J., Xiao, J.
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