Date:

Tuesday, September 20, 2016 - 2:00pm

Location:

Math Sci 111

Speaker:

Paata Ivanishvili (Kent State Univ)

Does the centered maximal function operator have a nontrivial fixed point in Lp over the n-dimensional Euclidean space? The answer is Yes if p>n/(n-2) with n>2, and No otherwise. However, if one considers other maximal functions, for example, uncentered (or ``almost centered'') maximal function operators defined over the family of shifts and dilates of a centrally symmetric convex body then the situation is much worse: we will show that for any n>0 and any p>1 there exists a constant A=A(p,n) strictly greater than one such that | Mf|_p > A |f|_p for any nonnegative f from Lp. In particular, this answers the question raised to the authors by Andrei Lerner.

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