Best weak--type $(p,p)$ constants, $1\leq p \leq 2$, for orthogonal harmonic functions and martingales
Janakiraman, Prabhu
Illinois J. Math., Tome 48 (2004) no. 3, p. 909-921 / Harvested from Project Euclid
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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 ¶ \[ K_p ={\left(\frac{1}{\pi}\int_{-\infty}^\infty \frac{{\left|\frac{2}{\pi} \log{|t|}\right|}^p}{t^2 + 1} dt\right)}^{-1}.\]
Publié le : 2004-07-15
Classification:  60G44,  43A15 
@article{1258131059,
     author = {Janakiraman, Prabhu},
     title = {Best weak--type $(p,p)$ constants, $1\leq p \leq 2$, for orthogonal harmonic functions and martingales},
     journal = {Illinois J. Math.},
     volume = {48},
     number = {3},
     year = {2004},
     pages = { 909-921},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258131059}
}

Janakiraman, Prabhu. Best weak--type $(p,p)$ constants, $1\leq p \leq 2$, for orthogonal harmonic functions and martingales. Illinois J. Math., Tome 48 (2004) no. 3, pp.  909-921. http://gdmltest.u-ga.fr/item/1258131059/