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math.FA1992
Two Remarks on Marcinkiewicz decompositions by Holomorphic Martingales
Paul F. X. Müller
The real part of $H^\infty(\bT)$ is not dense in $L^\infty_{\tR}(\bT)$. The John-Nirenberg theorem in combination with the Helson-Szegö theorem and the Hunt Muckenhaupt Wheeden the…
math.FA1992
Jean Bourgain's analytic partition of unity via holomorphic martingales
Paul F. X. Müller
Using stopping time arguments on holomorphic martingales we present a soft way of constructing J. Bourgain's analytic partitions of unity. Applications to Marcinkiewicz interploati…
math.FA1992
Permutations of the Haar system
Paul F. X. Müller
General permutations acting on the Haar system are investigated. We give a necessary and sufficient condition for permutations to induce an isomorphism on dyadic BMO. Extensions of…