{"title":"多元的分段单调函数及hardy和littlewood定理","authors":"M. I. D’yachenko","doi":"10.1070/IM1992V039N03ABEH002240","DOIUrl":null,"url":null,"abstract":"The author discusses classes of periodic functions of variables that are either piecewise monotonic or piecewise monotonic in the sense of Hardy, and clarifies the connections, for such functions, between the property of belonging to space, , and the convergence of series of their trigonometric Fourier coefficients, We establish the existence, when 1$ SRC=http://ej.iop.org/images/0025-5726/39/3/A02/tex_im_2240_img5.gif/>, of certain results that differ from the one-dimensional case.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"27 7","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"PIECEWISE MONOTONIC FUNCTIONS OF SEVERAL VARIABLES AND A THEOREM OF HARDY AND LITTLEWOOD\",\"authors\":\"M. I. D’yachenko\",\"doi\":\"10.1070/IM1992V039N03ABEH002240\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The author discusses classes of periodic functions of variables that are either piecewise monotonic or piecewise monotonic in the sense of Hardy, and clarifies the connections, for such functions, between the property of belonging to space, , and the convergence of series of their trigonometric Fourier coefficients, We establish the existence, when 1$ SRC=http://ej.iop.org/images/0025-5726/39/3/A02/tex_im_2240_img5.gif/>, of certain results that differ from the one-dimensional case.\",\"PeriodicalId\":159459,\"journal\":{\"name\":\"Mathematics of The Ussr-izvestiya\",\"volume\":\"27 7\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-izvestiya\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/IM1992V039N03ABEH002240\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-izvestiya","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/IM1992V039N03ABEH002240","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
PIECEWISE MONOTONIC FUNCTIONS OF SEVERAL VARIABLES AND A THEOREM OF HARDY AND LITTLEWOOD
The author discusses classes of periodic functions of variables that are either piecewise monotonic or piecewise monotonic in the sense of Hardy, and clarifies the connections, for such functions, between the property of belonging to space, , and the convergence of series of their trigonometric Fourier coefficients, We establish the existence, when 1$ SRC=http://ej.iop.org/images/0025-5726/39/3/A02/tex_im_2240_img5.gif/>, of certain results that differ from the one-dimensional case.
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