PreprintCC BY 4.0arXiv
A stochastic Carleson embedding theorem with constant e and the vector of Riesz transforms
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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BibTeX
@misc{domelevo2026stochastic,
title = {{A stochastic Carleson embedding theorem with constant $e$ and the vector of Riesz transforms}},
author = {Komla Domelevo and Johanna Fladung and Spyridon Kakaroumpas and Paul Montobbio and Stefanie Petermichl},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39919},
eprint = {2609.39919},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39919},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A stochastic Carleson embedding theorem with constant e and the vector of Riesz transforms
AU - Komla Domelevo
AU - Johanna Fladung
AU - Spyridon Kakaroumpas
AU - Paul Montobbio
AU - Stefanie Petermichl
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39919
UR - https://arxiv.org/abs/2609.39919
AB - 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.
ER -