{"title":"Weighted boundedness criteria for oscillatory integral operators via sharp maximal function estimates","authors":"Xi Cen","doi":"10.1007/s43034-026-00541-w","DOIUrl":null,"url":null,"abstract":"<div><p>We establish criteria for quantitative weighted Lebesgue estimates of oscillatory integral operators in different natural ranges of the decay order <i>m</i> via sharp maximal function estimates. Based on this, we further derive criteria for quantitative weighted bounds between weighted multi-exponent function spaces (including Besov–Lipschitz, Triebel–Lizorkin, and Sobolev spaces), also within the corresponding ranges of the decay order <i>m</i>. Our main results improve the decay range of some linear weighted estimates in Ferreira–Staubach [9, Mem. Amer. Math. Soc., 2014], Cao–Xue–Yabuta [5, J. Funct. Anal., 2020], Beltran–Cladek [3, J. Anal. Math., 2020], and Park–Tomita [20, J. Funct. Anal., 2024], and extend their conclusions to the aforementioned multi-exponent function spaces.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"17 4","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s43034-026-00541-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We establish criteria for quantitative weighted Lebesgue estimates of oscillatory integral operators in different natural ranges of the decay order m via sharp maximal function estimates. Based on this, we further derive criteria for quantitative weighted bounds between weighted multi-exponent function spaces (including Besov–Lipschitz, Triebel–Lizorkin, and Sobolev spaces), also within the corresponding ranges of the decay order m. Our main results improve the decay range of some linear weighted estimates in Ferreira–Staubach [9, Mem. Amer. Math. Soc., 2014], Cao–Xue–Yabuta [5, J. Funct. Anal., 2020], Beltran–Cladek [3, J. Anal. Math., 2020], and Park–Tomita [20, J. Funct. Anal., 2024], and extend their conclusions to the aforementioned multi-exponent function spaces.
期刊介绍：
Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group.
Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory.
Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.
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