Results 1 to 10 of about 36,617 (79)
Vanishing Mean Oscillation Spaces Associated with Operators Satisfying Davies-Gaffney Estimates [PDF]
Kyoto Journal of Mathematics, 2011 Let $(\mathcal{X}, d, \mu)$ be a metric measure space, $L$ a linear operator which has a bounded $H_\infty$ functional calculus and satisfies the Davies-Gaffney estimate, $\Phi$ a concave function on $(0,\infty)$ of critical lower type $p_\Phi^-\in(0,1]$
Liang, Yiyu, Yang, Dachun, Yuan, Wen
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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 J. Holden
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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.
Donald Sarason
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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
Donggao Deng +4 more
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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.
The Anh Bui
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Local vanishing mean oscillation
Bulletin de la Société mathématique 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
Almaz Butaev, Galia Dafni
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Holomorphic semigroups and Sarason’s characterization of vanishing mean oscillation
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.
Nikolaos Chalmoukis +1 more
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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.
K.‐J. Wirths, J. Xiao
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Vanishing mean oscillation and continuity of rearrangements
Advances in Mathematics, 2023 We 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, Galia Dafni, Ryan Gibara
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Graphs of maps between manifolds in trace spaces and with vanishing mean oscillation
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2013 We give a positive answer to a question raised by Alberti in connection with a recent result by Brezis and Nguyen. We show the existence of currents associated with graphs of maps in trace spaces that have vanishing mean oscillation. The degree of such maps may be written in terms of these currents, of which we give some structure properties.
E. Acerbi, Domenico Mucci
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