Open Access
December, 2018 Maximal Averages over Certain Non-smooth and Non-convex Hypersurfaces
Yaryong Heo, Sunggeum Hong, Chan Woo Yang
Taiwanese J. Math. 22(6): 1383-1401 (December, 2018). DOI: 10.11650/tjm/180204


We consider the maximal operators whose averages are taken over some non-smooth and non-convex hypersurfaces. For each $1 \leq i \leq d-1$, let $\phi_i \colon [-1,1] \to \mathbb{R}$ be a continuous function satisfying some derivative conditions, and let $\phi(y) = \sum_{i=1}^{d-1} \phi_i(y_i)$. We prove the $L^p$ boundedness of the maximal operators associated with the graph of $\phi$ which is a non-smooth and non-convex hypersurface in $\mathbb{R}^d$, $d \geq 3$.


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Yaryong Heo. Sunggeum Hong. Chan Woo Yang. "Maximal Averages over Certain Non-smooth and Non-convex Hypersurfaces." Taiwanese J. Math. 22 (6) 1383 - 1401, December, 2018.


Received: 4 July 2017; Revised: 5 February 2018; Accepted: 13 February 2018; Published: December, 2018
First available in Project Euclid: 14 March 2018

zbMATH: 07021695
MathSciNet: MR3878574
Digital Object Identifier: 10.11650/tjm/180204

Primary: 42B20
Secondary: 42B25

Keywords: maximal averages , non-smooth and non-convex hypersurfaces

Rights: Copyright © 2018 The Mathematical Society of the Republic of China

Vol.22 • No. 6 • December, 2018
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