On a singular integral estimate for the maximum modulus of a canonical product
Abi-Khuzam, Faruk F. ; Shayya, Bassam
Illinois J. Math., Tome 44 (2000) no. 4, p. 551-555 / Harvested from Project Euclid
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If $f$ is a canonical product with only real negative zeros and non-integral order $\rho,n(t,0)$ is the zero counting function, and $B(r,f)=\mathrm{sup}_{0 \lt \theta \lt \pi}|\log f(re^{i \theta})|$, then $$r^{-q-1}B(r,f) \leq \pi\{M \varphi(r) + MH\varphi(r)\}+\int_{0}^{\infty}{\frac{\varphi(t)dt}{t+r}},$$ where $\varphi(t) = t^{-q-1} n(t,0)$, $H$ is the Hilbert transform operator and $M$ is the Hardy-Littlewood maximal operator.
Publié le : 2000-09-15
Classification:  30D20,  30D35,  42A50 
@article{1256060415,
     author = {Abi-Khuzam, Faruk F. and Shayya, Bassam},
     title = {On a singular integral estimate for the maximum modulus of a canonical product},
     journal = {Illinois J. Math.},
     volume = {44},
     number = {4},
     year = {2000},
     pages = { 551-555},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1256060415}
}

Abi-Khuzam, Faruk F.; Shayya, Bassam. On a singular integral estimate for the maximum modulus of a canonical product. Illinois J. Math., Tome 44 (2000) no. 4, pp.  551-555. http://gdmltest.u-ga.fr/item/1256060415/