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arXiv · 2609.39919

A stochastic Carleson embedding theorem with constant $e$ and the vector of Riesz transforms

Komla Domelevo·Johanna Fladung·Spyridon Kakaroumpas·Paul Montobbio·Stefanie Petermichl
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Abstract

We prove a continuous-time Carleson embedding theorem with constant $e$ for a system of square-integrable continuous martingales whose quadratic covariations mimic the generalised Cauchy--Riemann relations. The argument is based on a Bellman function and a multidimensional Itô formula. As an application we transfer the estimate to the upper half-space via the Gundy--Varopoulos representation and obtain a Carleson embedding, still with constant $e$, for the vector consisting of a function and its Riesz transforms in arbitrary dimension.

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Komla Domelevo, Johanna Fladung, Spyridon Kakaroumpas, Paul Montobbio, Stefanie Petermichl. 2026-09-30. A stochastic Carleson embedding theorem with constant $e$ and the vector of Riesz transforms. https://arxiv.org/abs/2609.39919

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