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Absolutely Summing Operators Between Hardy Spaces

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dc.contributor.advisor Al-Masri, Ibrahim
dc.contributor.author Qunnais, Majeda
dc.date.accessioned 2019-04-09T06:43:03Z
dc.date.accessioned 2022-03-21T12:05:21Z
dc.date.accessioned 2022-05-11T05:39:07Z
dc.date.available 2019-04-09T06:43:03Z
dc.date.available 2022-03-21T12:05:21Z
dc.date.available 2022-05-11T05:39:07Z
dc.date.issued 1/1/2019
dc.identifier.uri http://test.ppu.edu/handle/123456789/1592
dc.description CD , no of pages 48, 31021 , mathematics 2/2019
dc.description.abstract The Hardy space Hp , 1 ≤ p ≤ ∞, is a subspace of L p that contain of all functions with Fourier series P∞ n=0 cne int. If a = (an) is a given vector, then the diagonal operator da : Hp → Hq is defined by da( P∞ n=0 cne inf ty) = P∞ n=0 ancne int . The absolutely summing operatoru : X → Y is a linear operator between Banach spaces. We say that u is p summing operator for 1 ≤ p ≤ ∞ if there is a constant c ≥ 0 such that regardless of the natural number m and regardless of the choice of x1, ..., xm in X we have, Xm i=1 kuxik p !1 p ≤ c.sup    Xm i=1 |φ(xi)| p !1 p , φ ∈ X 0 , kφk ≤ 1    (1) In this thesis, we consider the diagonal operator da between Hardy spaces Hp and Hq where 1 ≤ p, q ≤ ∞ and a is the sequence (an). In this thesis we find necessary and sufficient conditions for this diagonal operator to be 2 summing. We were able to prove that da : Hp → Hq is 2 summing if and only if a ∈ l 2 . After that, we prove that this operator is 1 summing if and only if a ∈ l 1 . en_US
dc.language.iso en en_US
dc.publisher جامعة بوليتكنك فلسطين - رياضيات en_US
dc.subject Hardy Spaces en_US
dc.title Absolutely Summing Operators Between Hardy Spaces en_US
dc.type Other en_US

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