Resumen:
Composition by a bi-Lipschitz measure-preserving map on the one-parameter
BMO space has been applied to study the Euler equation with a BMO-type
vorticity. We would like to discuss the same problem in the setting of biparameter
BMO space in R2. We will focus on composing by a rotation on the
biparameter BMO space. This BMO space is not preserved by a rotation since
it relies on the structure of axis-parallel rectangles. We will quantify this fact by
interpolation inequalities. One straightforward application of the interpolation
inequalities is a boundedness property of directional Hilbert transforms.
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