The convolution algebraH1(R) | Zendy

Raymond Johnson | Zendy; C. Robert Warner | Zendy

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The convolution algebraH¹(R)

Author(s) -

Raymond Johnson,

C. Robert Warner

Publication year - 2010

Publication title -

journal of function spaces

Language(s) - English

Resource type - Journals

eISSN - 2314-8896

pISSN - 2314-8888

DOI - 10.1155/2010/524036

Subject(s) - mathematics , banach algebra , identity (music) , convolution (computer science) , ideal (ethics) , banach space , maximal ideal , algebra over a field , pure mathematics , combinatorics , discrete mathematics , philosophy , physics , epistemology , machine learning , artificial neural network , acoustics , computer science

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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