{"title":"短广义德里赫特序列的解耦不等式","authors":"Yuqiu Fu, Larry Guth, Dominique Maldague","doi":"10.2140/apde.2023.16.2401","DOIUrl":null,"url":null,"abstract":"<p>We study decoupling theory for functions on <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ℝ</mi></math> with Fourier transform supported in a neighborhood of short Dirichlet sequences <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mrow><mo stretchy=\"false\">{</mo><mi>log</mi><mo> <!--FUNCTION APPLICATION--> </mo><!--nolimits--><mi>n</mi><mo stretchy=\"false\">}</mo></mrow><mrow><mi>n</mi><mo>=</mo><mi>N</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>N</mi><mo>+</mo><msup><mrow><mi>N</mi></mrow><mrow><mn>1</mn><mo>∕</mo><mn>2</mn></mrow></msup>\n</mrow></msubsup></math>, as well as sequences with similar convexity properties. We utilize the wave packet structure of functions with frequency support near an arithmetic progression. </p>","PeriodicalId":49277,"journal":{"name":"Analysis & PDE","volume":"11 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Decoupling inequalities for short generalized Dirichlet sequences\",\"authors\":\"Yuqiu Fu, Larry Guth, Dominique Maldague\",\"doi\":\"10.2140/apde.2023.16.2401\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study decoupling theory for functions on <math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>ℝ</mi></math> with Fourier transform supported in a neighborhood of short Dirichlet sequences <math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msubsup><mrow><mo stretchy=\\\"false\\\">{</mo><mi>log</mi><mo> <!--FUNCTION APPLICATION--> </mo><!--nolimits--><mi>n</mi><mo stretchy=\\\"false\\\">}</mo></mrow><mrow><mi>n</mi><mo>=</mo><mi>N</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>N</mi><mo>+</mo><msup><mrow><mi>N</mi></mrow><mrow><mn>1</mn><mo>∕</mo><mn>2</mn></mrow></msup>\\n</mrow></msubsup></math>, as well as sequences with similar convexity properties. We utilize the wave packet structure of functions with frequency support near an arithmetic progression. </p>\",\"PeriodicalId\":49277,\"journal\":{\"name\":\"Analysis & PDE\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-12-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis & PDE\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2140/apde.2023.16.2401\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis & PDE","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/apde.2023.16.2401","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Decoupling inequalities for short generalized Dirichlet sequences
We study decoupling theory for functions on with Fourier transform supported in a neighborhood of short Dirichlet sequences , as well as sequences with similar convexity properties. We utilize the wave packet structure of functions with frequency support near an arithmetic progression.
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