He received the Salem Prize in 1988 for his work in harmonic analysis.

[3] From 2007 to 2008 he was the Sir Edmund Whittaker Professor of Mathematical Science at the University of Edinburgh.

He was named to the 2021 class of fellows of the American Mathematical Society "for contributions to harmonic analysis and its relations to geometric measure theory".

[5] In 2024, the article "On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1",[6] by Fedor Nazarov, Xavier Tolsa, and Alexander Volberg has been selected by the International Congress of Basic Science, as a recipient of the 2024 Frontiers of Science Award in Mathematics.

This article about a Russian mathematician is a stub.