A note on maximal estimate for an oscillatory operator.
- Resource Type
- Article
- Source
Georgian Mathematical Journal . Jan2024, p1. 13p.- Subject
- Language
- ISSN
- 1072-947X
p. Then, using interpolation, we obtain the L p ( ℝ n ) {{{L^{p}({{\mathbb{R}^{n}}})}}} boundedness on T α , β ∗ {T_{\alpha,\beta}^{\ast}} when p > 1 {p>1} , which is an improvement of the recent result by Kenig and Staubach. At the critical case p = 1 {p=1} and β = n α 2 {\beta=\frac{n\alpha}{2}} , we show T α , β ∗ : B q ( ℝ n ) → L 1 , ∞ ( ℝ n ) {T_{\alpha,\beta}^{\ast}:B_{q}({\mathbb{R}^{n}})\rightarrow L^{1,\infty}({% \mathbb{R}^{n}})} , where B q ( ℝ n ) {B_{q}({\mathbb{R}^{n}})} is the block space introduced by Lu, Taibleson and Weiss in order to study the almost every convergence of the Bochner–Riesz means at the critical index. As a further application, we obtain the convergence speed of a combination to the fractional Schrödinger operators { e i t k | △ | α } {\{e^{itk|\triangle|^{\alpha}}\}} . [ABSTRACT FROM AUTHOR]