Ryan Gibara (Laval)

Title: Boundedness and continuity for rearrangements on spaces defined by mean oscillation.

Abstract: In joint work with Almut Burchard and Galia Dafni, we study the boundedness and continuity of rearrangement operators on the space BMO of functions of bounded mean oscillation. Improved bounds are obtained for the BMO-seminorm of the decreasing rearrangement, and the symmetric decreasing rearrangement is shown to be bounded on BMO. Both of these rearrangements are shown to be discontinuous as maps on BMO, but sufficient normalization conditions are established to guarantee continuity on the subspace VMO of functions of vanishing mean oscillation.
 

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