Asymptotic variance of the Beurling transform

symptotic variance can be used to measure the boundary behaviour of conformal maps and Bloch functions. A formula due to McMullen connects it to the Hausdorff dimension expansion of limit sets for certain dynamical families of conformal maps. We introduce the asymptotic variance of the Beurling transform as a tool for studying Hausdorff dimension of quasicircles at infinitesimal level. As a result, we find k-quasicircles with dimension bigger than 1+0.879k^2 for small k. An upper bound for this asymptotic variance can be deduced from Smirnov's quasicircle estimates. Finally, we also mention some very recent (and interesting) advances related to this topic. The talk is based on a joint paper with K. Astala, O. Ivrii and I. Prause

Digested slurry as a fertilizer for biogas ley

Digested slurry injected produces in this case comparable yields with mineral fertiliser. Because the primary growth is the largest and of the best quality it should be used for feed as the first option. The re-growths could then be used as a co-substrate in biogas reactors. Digested slurry is a good fertiliser for leys when injected. Injection of non-digested slurry reduces the ammonia emissions and leaching of soluble phosphorus but the significance of the low performance of nitrogen leaves open its fate

Volterra type integration operators from Bergman spaces to Hardy spaces

We completely characterize the boundedness of the Volterra type integration operators $J_b$ acting from the weighted Bergman spaces $A^p_\alpha$ to the Hardy spaces $H^q$ of the unit ball of $\mathbb{C}^n$ for all $0<p,q<\infty$. A partial solution to the case $n=1$ was previously obtained by Z. Wu in \cite{Wu}. We solve the cases left open there and extend all the results to the setting of arbitrary complex dimension $n$. Our tools involve area methods from harmonic analysis, Carleson measures and Kahane-Khinchine type inequalities, factorization tricks for tent spaces of sequences, as well as techniques and integral estimates related to Hardy and Bergman spaces.Comment: 26 pages, 1 figur

Lonkka- ja polviproteesit Suomessa 2010

19.10.201