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Seminar
FIELD Math:Analysis
DATE December 26 (Thu), 2019
TIME 11:10-12:10
PLACE 1503
SPEAKER Lee, Juyoung
HOST Jung, Joeun
INSTITUTE 서울대학교
TITLE Singular spherical maximal operators on a class of two step nilpotent Lie groups
ABSTRACT Let $ H^n \cong \mathbf{R}^{2n} \ltimes \mathbf{R}$ be the Heisenberg group and let $\mu_t$ be the normalized surface measure for the sphere of radius $t$ in $\mathbf{R}^{2n}$. Consider the maximal function defined by $Mf=\sup_{t>0}\vert f * \mu_t \vert$. We are interested in the boundedness property of this function on $L^p$-spaces. For $n\geq 2$, this maximal operator is bounded on $L^p$ when $p>\frac{2n}{2n-1}$. This result can be generalized to a more general class of surfaces and to groups satisfying a nondegeneracy condition. This talk is based on the paper written by D. M\"uller and A. Seeger.
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