Banach algebra of the Fourier multipliers on weighted Banach function spaces
Keyword(s):
AbstractLet MX,w(ℝ) denote the algebra of the Fourier multipliers on a separable weighted Banach function space X(ℝ,w).We prove that if the Cauchy singular integral operator S is bounded on X(ℝ, w), thenMX,w(ℝ) is continuously embedded into L∞(ℝ). An important consequence of the continuous embedding MX,w(ℝ) ⊂ L∞(ℝ) is that MX,w(ℝ) is a Banach algebra.
2009 ◽
Vol 7
(3)
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pp. 301-311
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2002 ◽
Vol 42
(1)
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pp. 57-89
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2000 ◽
Vol 38
(1)
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pp. 28-50
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2003 ◽
Vol 1
(1)
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pp. 45-59
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2007 ◽
Vol 49
(3)
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pp. 431-447
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