The Berezin transform of Toeplitz operators on the weighted Bergman space

In this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We characterize the bounded and compact Toeplitz operators on the weighted Bergman spaces with Békollé-Bonami weights in terms of Berezin transforms. Moreover, we estimate the essential norm of them assuming that they are bounded

Dominating sets and reverse Carleson measures on exponentially weighted Bergman spaces

We study the dominating sets and reverse Carleson measures on exponentially weighted Bergman spaces Apω under a new metric. Then, we give some applications of reverse Carleson measure and a generalization of Theorem 1 in Luecking [Sampling measures for Bergman spaces on the unit disk. Math Ann. 2000;316:659–679]

Glacial Area Changes in the Ili River Catchment (Northeastern Tian Shan) in Xinjiang, China, from the 1960s to 2009

The Ili River originates in the Tian Shan Mountains of Northwest China before flowing into Kazakhstan and Lake Balkash. Melting snow and ice are its major contributors. We analyzed glacial changes in the upper Ili River basin between the 1960s and 2007/2009 using topographic maps and satellite imagery from a Landsat TM. The relationships between glacial changes and glacial size, topographic factors, and debris cover were examined. Our results found that total glacial area decreased by 485 ± 177.3 km2 (24.2% ± 8.8%) during the study period, and there were no advancing glaciers. Additionally, 331 glaciers disappeared and 18 disintegrated into two or three smaller glaciers. This study demonstrated a linear relationship between glacial area change and elevation. Changes in glaciers smaller than 1 km2 were affected by both glacial size and topographic factors, while larger ones were affected by size only. Area losses in debris-covered glaciers were smaller by 2.5% to 7.5% compared to clean ice of the same size in this basin. As in other glaciated regions, glacial retreat in the Ili River basin is attributed to global warming. The slightly increasing precipitation over the study period could not offset the ice melting