کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4608212 | 1337915 | 2007 | 29 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Pointwise convergence of cone-like restricted two-dimensional (C,1) means of trigonometric Fourier series
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Pointwise convergence of cone-like restricted two-dimensional (C,1) means of trigonometric Fourier series Pointwise convergence of cone-like restricted two-dimensional (C,1) means of trigonometric Fourier series](/preview/png/4608212.png)
چکیده انگلیسی
The aim of this work is to generalize the more than 60 year old celebrated result of Marcinkiewicz and Zygmund on the convergence of the two-dimensional restricted (C,1) means of trigonometric Fourier series. They proved for any integrable function fâL1(T2) the a.e. convergenceÏ(n1,n2)fâfprovided n1/βâ¤n2â¤Î²n1, where β>1 is fixed constant. That is, the set of indices (n1,n2) remains in some positive cone around the identical function. We not only generalize this theorem, but give a necessary and sufficient condition for cone-like sets (of the set of indices) in order to preserve this convergence property.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 149, Issue 1, November 2007, Pages 74-102
Journal: Journal of Approximation Theory - Volume 149, Issue 1, November 2007, Pages 74-102
نویسندگان
György Gát,