{"title":"加权Orlicz空间中de la vall<s:1> - poussin均值的同时逼近性质","authors":"S. Jafarov","doi":"10.7153/JCA-2020-17-12","DOIUrl":null,"url":null,"abstract":"We investigate the simultaneous approximation properties of the de la Vallée-Poussin means in weighted Orlicz spaces in terms of the modulus of smoothness. In terms of the modulus of smoothness the direct theorem of simultaneous approximation is proved. Also, in weighted Orlicz spaces the modulus of smoothness are estimated from below and above in terms of n -th partial Fourier sums and de la Vallée-Poussin means.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":"189-198"},"PeriodicalIF":0.0000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Simultaneous approximation properties of de la Vallée-Poussin means in weighted Orlicz spaces\",\"authors\":\"S. Jafarov\",\"doi\":\"10.7153/JCA-2020-17-12\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate the simultaneous approximation properties of the de la Vallée-Poussin means in weighted Orlicz spaces in terms of the modulus of smoothness. In terms of the modulus of smoothness the direct theorem of simultaneous approximation is proved. Also, in weighted Orlicz spaces the modulus of smoothness are estimated from below and above in terms of n -th partial Fourier sums and de la Vallée-Poussin means.\",\"PeriodicalId\":73656,\"journal\":{\"name\":\"Journal of classical analysis\",\"volume\":\"1 1\",\"pages\":\"189-198\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of classical analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7153/JCA-2020-17-12\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of classical analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/JCA-2020-17-12","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们研究了加权Orlicz空间中de la vall - poussin均值在光滑模方面的同时逼近性质。从光滑模的角度，证明了同时逼近的直接定理。同样，在加权的Orlicz空间中，平滑的模量是根据n次偏傅里叶和和de la vall - poussin均值从下往上估计的。
Simultaneous approximation properties of de la Vallée-Poussin means in weighted Orlicz spaces
We investigate the simultaneous approximation properties of the de la Vallée-Poussin means in weighted Orlicz spaces in terms of the modulus of smoothness. In terms of the modulus of smoothness the direct theorem of simultaneous approximation is proved. Also, in weighted Orlicz spaces the modulus of smoothness are estimated from below and above in terms of n -th partial Fourier sums and de la Vallée-Poussin means.
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