Banach algebra of the Fourier multipliers on weighted Banach function spaces
Alexei Karlovich
Concrete Operators, Tome 2 (2015), / Harvested from The Polish Digital Mathematics Library
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Let 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.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:269960 
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     author = {Alexei Karlovich},
     title = {Banach algebra of the Fourier multipliers on weighted Banach function spaces},
     journal = {Concrete Operators},
     volume = {2},
     year = {2015},
     zbl = {1332.46040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_conop-2015-0001}
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Alexei Karlovich. Banach algebra of the Fourier multipliers on weighted Banach function spaces. Concrete Operators, Tome 2 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_conop-2015-0001/

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