Leonid Slavin, University of Cincinnati
1:00 PM - 2:00 PM
Let be either the heat or the Poisson kernel on and consider equipped with the norm
where denotes the -extension of a function on into the upper half-space:
We establish the following transference principle between the classical on an interval and If an integral functional admits an estimate on then exactly the same estimate holds for with all Euclidean averages replaced by -averages. In particular, all such estimates are dimension-free. The proof uses Bellman functions for as locally concave majorants for their -analogs, in conjunction with the probabilistic representation of the kernel Analogous results hold for related function classes, such as This is joint work with Pavel Zatitiskii.
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