Open Access
2023 Sharp estimates for martingale transforms with unbounded transforming sequences
Tomasz Gałązka, Adam Osękowski
Author Affiliations +
Electron. J. Probab. 28: 1-20 (2023). DOI: 10.1214/23-EJP953

Abstract

Suppose that p,q,r1 satisfy the condition 1p=1q+1r. The paper contains the identification of the best constants cp,q,r and Cp,q,r in the estimates

gp,cp,q,rfqvr,gpCp,q,rfqvr

where f is an arbitrary Hilbert-space valued martingale, g is its transform by a predictable sequence v, and v is the maximal function of v. This is extended to the more general context of differential subordination for continuous-time processes.

Funding Statement

T. Gałązka and A. Osękowski are supported by Narodowe Centrum Nauki (Poland), grant no. 2018/30/Q/ST1/00072.

Acknowledgments

The authors would like to thank Referee and the Associate Editor for the helpful suggestions, which led to the significant improvement of the presentation.

Citation

Download Citation

Tomasz Gałązka. Adam Osękowski. "Sharp estimates for martingale transforms with unbounded transforming sequences." Electron. J. Probab. 28 1 - 20, 2023. https://doi.org/10.1214/23-EJP953

Information

Received: 16 February 2022; Accepted: 1 May 2023; Published: 2023
First available in Project Euclid: 10 May 2023

MathSciNet: MR4586651
Digital Object Identifier: 10.1214/23-EJP953

Subjects:
Primary: 60G42 , 60G44

Keywords: best constants , Burkholder’s method , Differential subordination , martingale , transform

Vol.28 • 2023
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