Continuous-time sparse domination

Komla Domelevo; Stefanie Petermichl

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arXiv · 1607.06319

Continuous-time sparse domination

Komla Domelevo·Stefanie Petermichl

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Abstract

We develop the self similarity argument known as sparse domination in an abstract martingale setting, using a continuous time parameter. With this method, we prove a sharp weighted L^p estimate for the maximal operator Y^* of Y with respect to X. Here Y and X are uniformly integrable c\`adll\`ag Hilbert space valued martingales and Y differentially subordinate to X via the square bracket process. We also present a second, very simple proof of the special case Y=X. In this generality, notably including processes with jumps, the special case Y = X addresses a question raised in the late 70s by Bonami--L\'epingle.

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Komla Domelevo, Stefanie Petermichl. 2016-07-21. Continuous-time sparse domination. https://arxiv.org/abs/1607.06319

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