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On maximal operators along surfaces

Authors:

Hung Viet Le

Institution:

(1) Mathematics Department, Oregon State University, 368 Kidder Hall, 97331-4605 Corvallis, OR

Abstract:

In this paper, we establish the boundedness of the following maximal operator

$Mf(x,x_n ) = \mathop {\sup }\limits_{r > 0} \left\{ {\frac{1}{{r^{n - 1} }}\int_{\left| y \right| \leqslant r} {\left| {f(x - y,x_n - \Gamma (y))} \right|dy} } \right\}(x,y \in R^{n - 1} ,x_n \in R)$

onL ^p (R ⁿ) for allp>1, n≥2, where Γ(y)≡Γ(|y|) is a real, measurable, and radial function defined onR ⁿ⁻¹.

Keywords:

1991 Mathematics Subject Classification" target="_blank">1991 Mathematics Subject Classification 42B20 42B25

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