Hedenmalm has mainly contributed to the development of the theory of Bergman spaces and the associated reproducing kernels in one complex variable.
[1][2] Later, in 2018, he was elected to DKNVS, the Royal Norwegian Society of Sciences and Letters in Trondheim.
Hedenmalm has collaborated with a number of other mathematicians, in particular with Alexander Borichev, Serguei Shimorin and Nikolai Makarov.
He received the Wallenberg Prize in 1992, and in 1996 he was invited speaker at 2ECM (second European Congress of Mathematicians) in Budapest.
In 2015, he received the Eva and Lars Gårding Prize from KFS, the Royal Physiographic Society in Lund.