Subordination by orthogonal martingales in \(L^{p}\) and zeros of Laguerre polynomials

In this paper we address the question of finding the best \(L^p\)-norm constant for martingale transforms with one-sided orthogonality. We consider two martingales on a probability space with filtration \(\mathcal{B}\) generated by a two-dimensional Brownian motion \(B_t\). One is differentially sub...

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Bibliographic Details
Published in:arXiv.org 2011-09
Main Authors: Borichev, Alexander, Janakiraman, Prabhu, Volberg, Alexander
Format: Article
Language:English
Subjects:
Brownian motion
Martingales
Orthogonality
Polynomials
Three dimensional motion
Online Access:Get full text
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Summary:In this paper we address the question of finding the best \(L^p\)-norm constant for martingale transforms with one-sided orthogonality. We consider two martingales on a probability space with filtration \(\mathcal{B}\) generated by a two-dimensional Brownian motion \(B_t\). One is differentially subordinated to the other. Here we find the sharp estimate for subordinate martingales if the subordinated martingale is orthogonal and \(1
ISSN:2331-8422
DOI:10.48550/arxiv.1012.0943