Research interests:
Singular integral operators, maximal functions, weights, Hardy spaces, and BMO.
The main focus has been on the Bellman functions and the related questions of
transference between results for martingales and their continuous analogs. Most
recent interests are in Monge-Amp\`{e}re equations arising in Bellman
contexts
and connections between the geometry of developable surfaces and
optimizers
in sharp inequalities; dimension-free estimates for averaging classes
associated
with semigroup kernels; best dimensional estimates in weak-type inequalities;
non-infinitesimal and non-autonomous Bellman functions; sharp estimates on trees; the Erd\H{o}s--Falconer
conjecture on the sphere; and the Beurling--Ahlfors transform in higher dimensions.
Contact information
Department of Mathematical Sciences
French Hall West
University of Cincinnati
2815 Commons Way
Cincinnati, OH 45221
Office: Phone: email: webpage:
5428E French Hall
513 556 4125
leonid.slavin(at)uc.edu
http://homepages.uc.edu/~slavinld