Article contents
$L^{p}$ BOUNDS FOR NONISOTROPIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES
Published online by Cambridge University Press: 17 August 2015
Abstract
In an extrapolation argument, we prove certain $L^{p}\,(1<p<\infty )$ estimates for nonisotropic Marcinkiewicz operators associated to surfaces under the integral kernels given by the elliptic sphere functions
${\rm\Omega}\in L(\log ^{+}L)^{{\it\alpha}}({\rm\Sigma})$ and the radial function
$h\in {\mathcal{N}}_{{\it\beta}}(\mathbb{R}^{+})$. As applications, the corresponding results for parametric Marcinkiewicz integral operators related to area integrals and Littlewood–Paley
$g_{{\it\lambda}}^{\ast }$-functions are given.
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 99 , Issue 3 , December 2015 , pp. 380 - 398
- Copyright
- © 2015 Australian Mathematical Publishing Association Inc.
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