A Weak-Type Inequality for Orthogonal Submartingales and Subharmonic Functions

Adam Osękowski

Bulletin of the Polish Academy of Sciences. Mathematics (2011)

• Volume: 59, Issue: 3, page 261-274
• ISSN: 0239-7269

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Abstract

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Let X be a submartingale starting from 0, and Y be a semimartingale which is orthogonal and strongly differentially subordinate to X. The paper contains the proof of the sharp estimate $\mathbb{P}\left(su{p}_{t\ge 0}\right|Y_t\left|\ge 1\right)\le 3.375...\parallel X\parallel ₁$. As an application, a related weak-type inequality for smooth functions on Euclidean domains is established.

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Adam Osękowski. "A Weak-Type Inequality for Orthogonal Submartingales and Subharmonic Functions." Bulletin of the Polish Academy of Sciences. Mathematics 59.3 (2011): 261-274. <http://eudml.org/doc/281126>.

@article{AdamOsękowski2011,
abstract = {Let X be a submartingale starting from 0, and Y be a semimartingale which is orthogonal and strongly differentially subordinate to X. The paper contains the proof of the sharp estimate $ℙ(sup_\{t≥0\} |Y_t| ≥ 1) ≤ 3.375... ∥X∥₁$. As an application, a related weak-type inequality for smooth functions on Euclidean domains is established.},
author = {Adam Osękowski},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {submartingale; subharmonic function; strong differential subordination; weak type inequality; best constants},
language = {eng},
number = {3},
pages = {261-274},
title = {A Weak-Type Inequality for Orthogonal Submartingales and Subharmonic Functions},
url = {http://eudml.org/doc/281126},
volume = {59},
year = {2011},
}

TY - JOUR
AU - Adam Osękowski
TI - A Weak-Type Inequality for Orthogonal Submartingales and Subharmonic Functions
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2011
VL - 59
IS - 3
SP - 261
EP - 274
AB - Let X be a submartingale starting from 0, and Y be a semimartingale which is orthogonal and strongly differentially subordinate to X. The paper contains the proof of the sharp estimate $ℙ(sup_{t≥0} |Y_t| ≥ 1) ≤ 3.375... ∥X∥₁$. As an application, a related weak-type inequality for smooth functions on Euclidean domains is established.
LA - eng
KW - submartingale; subharmonic function; strong differential subordination; weak type inequality; best constants
UR - http://eudml.org/doc/281126
ER -

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