The boundedness of Bochner-Riesz operators on the weighted weak Hardy spaces

2011/11/06 by Hua Wang, Wang, Hua
Mathematics · Social Sciences · #42B15 #42B25 #42B30 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Polish Law and Legal System

paper · pdf · doi:10.48550/arxiv.1111.1388

openalex publication_date 2011/11/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let w be a Muckenhoupt weight and WH^p_w(\mathbb Rⁿ) be the weighted weak Hardy spaces. In this paper, by using the atomic decomposition of WH^p_w(\mathbb Rⁿ), we will show that the maximal Bochner-Riesz operators T^δ_* are bounded from WH^p_w(\mathbb Rⁿ) to WL^p_w(\mathbb Rⁿ) when 0n/p-(n+1)/2. Moreover, we will also prove that the Bochner-Riesz operators T^δ_R are bounded on WH^p_w(\mathbb Rⁿ) for 0n/p-(n+1)/2. Our results are new even in the unweighted case.

Citations

• Weighted norm inequalities for the conjugate function and Hilbert transform

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