The convolution algebra H1(R)
H1(R) is a Banach algebra which has better mapping properties under singular integrals than L1(R) . We show that its approximate identity sequences are unbounded by constructing one unbounded approximate identity sequence {vn}. We introduce a Banach algebra Q that properly lies between H1 and L1, an...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2010-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2010/524036 |
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doaj-d81cdaf0245f48659435c2fe2d9f598f2020-11-24T21:00:00ZengHindawi LimitedJournal of Function Spaces and Applications0972-68022010-01-018216717910.1155/2010/524036The convolution algebra H1(R)R. L. Johnson0C. R. Warner1University of Maryland, College Park, MD 20742-4105, USAUniversity of Maryland, College Park, MD 20742-4105, USAH1(R) is a Banach algebra which has better mapping properties under singular integrals than L1(R) . We show that its approximate identity sequences are unbounded by constructing one unbounded approximate identity sequence {vn}. We introduce a Banach algebra Q that properly lies between H1 and L1, and use it to show that c(1 + ln n) ≤ ||vn||H1 ≤ Cn1/2. We identify the maximal ideal space of H1 and give the appropriate version of Wiener's Tauberian theorem.http://dx.doi.org/10.1155/2010/524036 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
R. L. Johnson C. R. Warner |
| spellingShingle |
R. L. Johnson C. R. Warner The convolution algebra H1(R) Journal of Function Spaces and Applications |
| author_facet |
R. L. Johnson C. R. Warner |
| author_sort |
R. L. Johnson |
| title |
The convolution algebra H1(R) |
| title_short |
The convolution algebra H1(R) |
| title_full |
The convolution algebra H1(R) |
| title_fullStr |
The convolution algebra H1(R) |
| title_full_unstemmed |
The convolution algebra H1(R) |
| title_sort |
convolution algebra h1(r) |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces and Applications |
| issn |
0972-6802 |
| publishDate |
2010-01-01 |
| description |
H1(R) is a Banach algebra which has better mapping properties under singular integrals than L1(R) . We show that its approximate identity sequences are unbounded by constructing one unbounded approximate identity sequence {vn}. We introduce a Banach algebra Q that properly lies between H1 and L1, and use it to show that c(1 + ln n) ≤ ||vn||H1 ≤ Cn1/2. We identify the maximal ideal space of H1 and give the appropriate version of Wiener's Tauberian theorem. |
| url |
http://dx.doi.org/10.1155/2010/524036 |
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AT rljohnson theconvolutionalgebrah1r AT crwarner theconvolutionalgebrah1r AT rljohnson convolutionalgebrah1r AT crwarner convolutionalgebrah1r |
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