46 citations · 55 across the 14 of their papers we have counts for
16 papers
A Dyadic Approach to Weak Characterizations of Function Spaces
Galia Dafni, Shahaboddin Shaabani
Weak-type quasi-norms are defined using the mean oscillation or the mean of a function on dyadic cubes, providing discrete analogues and variants of the corresponding quasi-norms o…
boundedness of Localized Operators and Commutators with bmo and lmo
Galia Dafni, Chun Ho Lau
We first consider two types of localizations of singular integral operators of convolution type, and show, under mild decay and smoothness conditions on the auxiliary functions, th…
Necessary cancellation conditions for the boundedness of operators on local Hardy spaces
Galia Dafni, Chun Ho Lau, Tiago Picon +1
In this work we present necessary cancellation conditions for the continuity of linear operators in , , that map atoms into pseudo-molecules. Our nece…
Local vanishing mean oscillation
Almaz Butaev, Galia Dafni
We consider various notions of vanishing mean oscillation on a (possibly unbounded) domain , and prove an analogue of Sarason's theorem, giving sufficient co…
Vanishing Mean Oscillation and Continuity of Rearrangements
Almut Burchard, Galia Dafni, Ryan Gibara
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 o…
Inhomogeneous cancellation conditions and Calderón-Zygmund type operators on
Galia Dafni, Chun Ho Lau, Tiago Picon +1
In this work we present a new approach to molecules on Goldberg's local Hardy spaces , , assuming an appropriate cancellation condition. As application…
Locally uniform domains and extension of bmo functions
Almaz Butaev, Galia Dafni
We prove that for a domain , being in the sense of Jones is equivalent to being an extension domain for bmo, the nonhonomogeneous version of the…
BMO and the John-Nirenberg Inequality on Measure Spaces
Galia Dafni, Ryan Gibara, Andrew Lavigne
We study the space BMO in the general setting of a measure space with a fixed collection of measurable sets of positive and finite measure, consisting of…
Mean oscillation bounds on rearrangements
Almut Burchard, Galia Dafni, Ryan Gibara
We use geometric arguments to prove explicit bounds on the mean oscillation for two important rearrangements on . For the decreasing rearrangement of a rearrang…
A note on decreasing rearrangement and mean oscillation on measure spaces
Almut Burchard, Galia Dafni, Ryan Gibara
We derive bounds on the mean oscillation of the decreasing rearrangement on in terms of the mean oscillation of on a suitable measure space . In the spe…
Geometric maximal operators and BMO on product bases
Galia Dafni, Ryan Gibara, Hong Yue
We consider the problem of the boundedness of maximal operators on BMO on shapes in . We prove that for bases of shapes with an engulfing property, the corresponding…
BMO on shapes and sharp constants
Galia Dafni, Ryan Gibara
We consider a very general definition of BMO on a domain in , where the mean oscillation is taken with respect to a basis of shapes, i.e. a collection of open sets co…
On the extension of VMO functions
Almaz Butaev, Galia Dafni
We consider functions of vanishing mean oscillation on a bounded domain and prove a analogue of the extension theorem of P. Jones for . We show that if…
The space : nontriviality and duality
Galia Dafni, Tuomas Hytönen, Riikka Korte +1
We study a function space based on a condition introduced by John and Nirenberg as a variant of BMO. It is known that , but otherwi…
An atomic decomposition of the Hajłasz Sobolev space $\Mone$ on manifolds
Nadine Badr, Galia Dafni
Several possible notions of Hardy-Sobolev spaces on a Riemannian manifold with a doubling measure are considered. Under the assumption of a Poincaré inequality, the space $\Mone$,…
Classes of Measures Generated by Capacities
G. Dafni, G. E. Karadzhov, J. Xiao
We introduce classes of measures in the half-space generated by Riesz, or Bessel, or Besov capacities in , and give a geometric characterization…