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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.39919

Authors: Domelevo, Komla, Fladung, Johanna, Kakaroumpas, Spyridon, Montobbio, Paul, Petermichl, Stefanie

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7215088124

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