Hp-Maximal Regularity and Operator Valued Multipliers on Hardy Spaces
2007 ◽
Vol 59
(6)
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pp. 1207-1222
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Keyword(s):
AbstractWe consider maximal regularity in the Hp sense for the Cauchy problem u′(t) + Au(t) = f(t) (t ∈ ℝ), where A is a closed operator on a Banach space X and f is an X-valued function defined on ℝ. We prove that if X is an AUMD Banach space, then A satisfies Hp-maximal regularity if and only if A is Rademacher sectorial of type < . Moreover we find an operator A with Hp-maximal regularity that does not have the classical Lp-maximal regularity. We prove a related Mikhlin type theorem for operator valued Fourier multipliers on Hardy spaces Hp(ℝ X), in the case when X is an AUMD Banach space.
Keyword(s):
2018 ◽
Vol 34
(4)
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pp. 1541-1561
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1986 ◽
Vol 33
(3)
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pp. 407-418
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2015 ◽
Vol 3
(5)
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pp. 32-36
Keyword(s):
2018 ◽
Vol 62
(4)
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pp. 391-397
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Keyword(s):
2013 ◽
Vol 2013
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pp. 1-16
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