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arXiv · 1410.8786

Localization and projections on bi-parameter BMO

Richard Lechner·Paul F. X. Müller
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Abstract

We prove that for any operator $T$ on bi--parameter BMO the identity factors through $T$ or $I - T$. Bourgain's localization method provides the conceptual framework of our proof. It consists in replacing the factorization problem on the non--separable bi--parameter BMO by its localized, finite dimensional counterpart. We solve the resulting finite dimensional factorization problems by exploiting the geometry and combinatorics of colored dyadic rectangles.

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Richard Lechner, Paul F. X. Müller. 2014-10-31. Localization and projections on bi-parameter BMO. https://doi.org/10.1093/qmath%2Fhav028

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