Some one-sided estimates for oscillatory singular integrals

2014/09/20 by Zunwei Fu, Shanzhen Lu, Fu, Zunwei +5
Mathematics · #42B20 #42B25 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #math.CA #math.FA #msc:42B20 #msc:42B25

paper · pdf · doi:10.48550/arxiv.1410.3379

24 pages, Nonlinear Anal. 2014

arxiv created 2014/09/20 · openalex publication_date 2014/09/20 · arxiv updated 2014/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to establish some one-sided estimates for oscillatory singular integrals. The boundedness of certain oscillatory singular integral on weighted Hardy spaces H¹₊(w) is proved. It is here also show that the H¹₊(w) theory of oscillatory singular integrals above cannot be extended to the case of H^q₊(w) when 0<q<1 and w∈ A_p⁺, a wider weight class than the classical Muckenhoupt class. Furthermore, a criterion on the weighted L^p-boundednesss of the oscillatory singular integral is given.

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