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- W4300501855 abstract "The motivation for this paper comes from the following question on comparison of norms of conformal martingales $X$, $Y$ in $R^d$, $dgeq 2$. Suppose that $Y$ is differentially subordinate to $X$. For $0<p<infty$, what is the optimal value of the constant $C_{p,d}$ in the inequality $$ Y_pleq C_{p,d}X_p ?$$ We answer this question by considering a more general related problem for nonnegative submartingales. This enables us to study extension of the above inequality to the case when $d>1$ is not an integer, which has further interesting applications to stopped Bessel processes and to the behavior of smooth functions on Euclidean domains. The inequality for conformal martingales, which has its roots on the study of the $L^p$ norms of the Beurling-Ahlfors singular integral operator cite{BW}, extends a recent result of Borichev, Janakiraman and Volberg cite{BJV2}." @default.
- W4300501855 created "2022-10-03" @default.
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- W4300501855 date "2011-12-02" @default.
- W4300501855 modified "2023-09-27" @default.
- W4300501855 title "Burkholder inequalities for submartingales, Bessel processes and conformal martingales" @default.
- W4300501855 doi "https://doi.org/10.48550/arxiv.1112.0551" @default.
- W4300501855 hasPublicationYear "2011" @default.
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