On the convolution operators arising in the study of abstract initial boundary value problems
1996 ◽
Vol 126
(3)
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pp. 515-539
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Keyword(s):
We consider convolution operators arising in the study of abstract initial boundary value problems. These operators are of the formwhere {S(t)}t ≧0 is a C0-semigroup in a Banach space X,, with infinitesimal generator A0,: D(A0), ⊂ X, → X, and K(z): Y → X is a linxear, continuous mapping defined in another Banach space Y., We study the continuity of T between the spaces Lp([0, + ∞), Y), and Lq([0, + ∞), X), 1 ≦ p, q, ≦ + ∞. We give several examples of the applicability of the results to some familiar initial boundary value problems, including both parabolic and hyperbolic cases.
2004 ◽
Vol 134
(1)
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pp. 1-9
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2018 ◽
Vol 16
(1)
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pp. 19-43
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2000 ◽
Vol 54
(5-6)
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pp. 9-27
2001 ◽
Vol 56
(8-9)
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pp. 21
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2018 ◽
Vol 77
(18)
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pp. 1581-1595
1966 ◽
Vol 14
(3)
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pp. 302-307
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