Abstract
We prove that the best weak-type $(p,p)$ constant, $1\leq p\leq 2$, for orthogonal harmonic functions $u$ and $v$ with $v$ differentially subordinate to $u$ is
\[ K_p ={\left(\frac{1}{\pi}\int_{-\infty}^\infty \frac{{\left|\frac{2}{\pi} \log{|t|}\right|}^p}{t^2 + 1} dt\right)}^{-1}.\]
Citation
Prabhu Janakiraman. "Best weak--type $(p,p)$ constants, $1\leq p \leq 2$, for orthogonal harmonic functions and martingales." Illinois J. Math. 48 (3) 909 - 921, Fall 2004. https://doi.org/10.1215/ijm/1258131059
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