The present study investigated how climate and plant size affect the growth of Bauhinia thonningii and how fire and source of regeneration (grown from coppice versus seedlings) might modify the results. The study was conducted over a period of 10 y, from 1997 to 2007, at a savanna site in central Zambia. Trees were marked and monitored throughout the entire period; they showed a phase of declining growth (1998–2003) and a phase of low growth (2004–2007). During the phase of declining growth autocorrelation was high but either weakened or disappeared during the phase of low growth. After adjusting data for autocorrelation, climate factors and tree size accounted for between 14% and 35% of the variation in annual tree radial growth. However, the growth responses of trees to climate factors and tree size varied with the source of regeneration (i.e. coppice or seedling) and fire treatment. Trees of seedling origin were only affected by climate factors and tree size when exposed to annual burning whereas all trees of coppice origin were significantly affected by climate factors and tree size, regardless of the fire treatment. However, basal radial growth of saplings that were monitored for 4 y (2003–2007) was significantly influenced by maximum temperature and rainfall that accounted for 33–47% of the variance in annual radial growth under fire protection. Saplings recovered from shoot die-back during the cool dry season by resprouting in the hot dry season and this annual die-back slowed the height growth of B. thonningii saplings.

For 0 < p < ∞, we let pp−1 denote the space of those functions f that are analytic in the unit disc Δ = {z ∈ C: |z| < 1} and satisfy ∫Δ(1 – |z|)p−1|f′(z)|pdx dy < ∞ The spaces pp−1 are closely related to Hardy spaces. We have, p−1p ⊂ Hp, if 0 < p ≦ 2, and Hp ⊂ pp−1, if 2 ≦ p < ∞. In this paper we obtain a number of results about the Taylor coefficients of pp-1 -functions and sharp estimates on the growth of the integral means and the radial growth of these functions as well as information on their zero sets.

2000 Mathematics subject classification: primary 30D35, 30D55, 46E15.

Some results are presented relating to questions raised in a recent paper by Anderson, Hayman and Pommerenke regarding the size of the set of boundary points of the unit disc at which a univalent function has a prescribed radial growth.

AMS 2000 Mathematics subject classification: Primary 30C55

Fire is the most prevalent form of disturbance in the cerrado savannas of south-central Brazil, commonly occurring at 2-to 3-y intervals (Coutinho 1990). Frequent fires are known to increase tree mortality (Sato & Miranda 1996), but it is unclear how they affect the growth of the surviving trees. Damage to the crown from scorching is likely to have a direct negative effect on plant growth, however the reduction in tree density due to repeated burning could indirectly stimulate growth because of release from competition. Understanding the relative strength of these contrasting direct and indirect effects of fire on tree growth is important for predicting human impacts on the cerrado vegetation.