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Littlewood-Paley equivalence and homogeneous Fourier multipliers (1601.03173v1)
Published 13 Jan 2016 in math.CA
Abstract: We consider certain Littlewood-Paley operators and prove characterization of some function spaces in terms of those operators. When treating weighted Lebesgue spaces, a generalization to weighted spaces will be made for H\"ormander's theorem on the invertibility of homogeneous Fourier multipliers. Also, applications to the theory of Sobolev spaces will be given.
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