Affiliation:
1. Department of Mathematics Guangdong University of Petrochemical Technology Maoming Guangdong China
2. Department of Mathematics Shantou University Shantou Guangdong China
3. Department of Mathematics Jiaying University Meizhou Guangdong China
Abstract
Using Khinchin's inequality, Geršgorin's theorem, and the atomic decomposition of Bergman spaces, we estimate the norm and essential norm of Stević–Sharma‐type operators between weighted Bergman spaces
and
and the sum of weighted differentiation composition operators with different symbols from the weighted Bergman spaces
to
. The estimates of those between Bergman spaces remove all the restrictions of a result of Stevic, Sharma, and Bhat. As a by‐product, we also get an interpolation theorem for Bergman spaces induced by doubling weights.
Funder
National Natural Science Foundation of China
Basic and Applied Basic Research Foundation of Guangdong Province