Proceedings of the Japan Academy, Series A. Mathematical Sciences | |
Weighted inequalities for spherical maximal operator | |
article | |
Ramesh Manna1  | |
[1] School of Mathematics, Harish-Chandra Research Institute | |
关键词: Spherical maximal operator; oscillatory integrals; Ap weights.; | |
DOI : 10.3792/pjaa.91.135 | |
学科分类:数学(综合) | |
来源: Japan Academy | |
【 摘 要 】
Given a set $E=(0, \infty)$, the spherical maximal operator $\mathcal{M}$ associated to the parameter set $E$ is defined as the supremum of the spherical means of a function when the radii of the spheres are in $E$. The aim of this paper is to study the following inequality \begin{equation} ∫_{\mathbf{R}^{n}} (\mathcal{M}f(x))^{p} φ(x) dx ≤ B_{p} ∫_{\mathbf{R}^{n}} |f(x)|^{p} φ(x) dx, \label{Lb1} \end{equation} holds for $p > \frac{2n}{n-1}$ with the continuous spherical maximal operator $\mathcal{M}$ and where the nonnegative function $\phi$ is in some weights obtained from the $A_{p}$ classes. As an application, we will get the boundedness of vector-valued extension of the spherical means.
【 授权许可】
Unknown
【 预 览 】
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