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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 0972-6802 |