Restrictions and extensions of Fourier multipliers
Max Jodeit (1970)
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Max Jodeit (1970)
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David Shreve (1975)
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David Shreve (1976)
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Charles McCarthy (1974)
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Richard Rubin (1978)
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Ronald Coifman, Guido Weiss (1973)
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Richard Wheeden (1966)
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Carl Herz, Nestor Rivière (1972)
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Carlos Lizama, Rodrigo Ponce (2011)
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Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multiplier theorems, we obtain necessary and sufficient conditions for the existence and uniqueness of periodic solutions to the equation d/dt(Mu(t)) = Au(t) + f(t), in terms of either boundedness or R-boundedness of the modified resolvent operator determined by the equation. Our results are obtained in the scales of periodic Besov and periodic Lebesgue vector-valued spaces. ...
Garth Gaudey, Ian Inglis (1979)
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Yang-Chun Chang, P. Tomas (1984)
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Verónica Poblete, Juan C. Pozo (2013)
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Using operator valued Fourier multipliers, we characterize maximal regularity for the abstract third-order differential equation αu'''(t) + u''(t) = βAu(t) + γBu'(t) + f(t) with boundary conditions u(0) = u(2π), u'(0) = u'(2π) and u''(0) = u''(2π), where A and B are closed linear operators defined on a Banach space X, α,β,γ ∈ ℝ₊, and f belongs to either periodic Lebesgue spaces, or periodic Besov spaces, or periodic Triebel-Lizorkin spaces.