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math.CA2013
Weighted Local Estimates for Singular Integral Operators
Jonathan Poelhuis, Alberto Torchinsky
A local median decomposition is used to prove that a weighted local mean of a function is controlled by a weighted local mean of its local sharp maximal function. Together with (a…
math.CA2012
On a Local Mean Oscillation Decomposition
Jonathan Poelhuis, Alberto Torchinsky
In this note we generate two local median oscillation decompositions of an arbitrary measurable function and discuss some applications to Calderón-Zygmund singular integral operato…
math.CA2012
Medians, Continuity, and Oscillation
Jonathan Poelhuis, Alberto Torchinsky
In this paper we consider properties of medians as they pertain to the continuity and vanishing oscillation of a function. Our approach is based on the observation that medians are…