Summation of Multiple Fourier Series in Matrix Weighted -Spaces

Summation of Multiple Fourier Series in Matrix Weighted -Spaces

This paper is concerned with rectangular summation of multiple Fourier series in matrix weighted -spaces. We introduce a product Muckenhoupt condition for matrix weights and prove that rectangular Fourier partial sums converge in the corresponding matrix weighted space , , if and only if the weigh...

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Main Author: Morten Nielsen
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2013/135245
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spelling doaj-7553e87dece04de5ac50abb1b2a9119c2020-11-24T21:47:54ZengHindawi LimitedJournal of Mathematics2314-46292314-47852013-01-01201310.1155/2013/135245135245Summation of Multiple Fourier Series in Matrix Weighted -SpacesMorten Nielsen0Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220 Aalborg East, DenmarkThis paper is concerned with rectangular summation of multiple Fourier series in matrix weighted -spaces. We introduce a product Muckenhoupt condition for matrix weights and prove that rectangular Fourier partial sums converge in the corresponding matrix weighted space , , if and only if the weight satisfies the product Muckenhoupt condition. The same result is shown to hold true for other summation methods such as Cesàro and summation with the Jackson kernel.http://dx.doi.org/10.1155/2013/135245
collection DOAJ
language English
format Article
sources DOAJ
author Morten Nielsen
spellingShingle Morten Nielsen
Summation of Multiple Fourier Series in Matrix Weighted -Spaces
Journal of Mathematics
author_facet Morten Nielsen
author_sort Morten Nielsen
title Summation of Multiple Fourier Series in Matrix Weighted -Spaces
title_short Summation of Multiple Fourier Series in Matrix Weighted -Spaces
title_full Summation of Multiple Fourier Series in Matrix Weighted -Spaces
title_fullStr Summation of Multiple Fourier Series in Matrix Weighted -Spaces
title_full_unstemmed Summation of Multiple Fourier Series in Matrix Weighted -Spaces
title_sort summation of multiple fourier series in matrix weighted -spaces
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4629
2314-4785
publishDate 2013-01-01
description This paper is concerned with rectangular summation of multiple Fourier series in matrix weighted -spaces. We introduce a product Muckenhoupt condition for matrix weights and prove that rectangular Fourier partial sums converge in the corresponding matrix weighted space , , if and only if the weight satisfies the product Muckenhoupt condition. The same result is shown to hold true for other summation methods such as Cesàro and summation with the Jackson kernel.
url http://dx.doi.org/10.1155/2013/135245
work_keys_str_mv AT mortennielsen summationofmultiplefourierseriesinmatrixweightedspaces
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