5 citations · 6 across the 5 of their papers we have counts for
7 papers
Fractional maximal functions and mean oscillation on bounded doubling metric measure spaces
Ryan Gibara, Josh Kline
Let be a doubling metric measure space. We consider the behaviour of the fractional maximal function for , where is the doubling dimension, acting on…
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…
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…