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- W2042118456 abstract "Let G be a locally compact abelian group and let μ be a complex valued regular Borel measure on G. In this paper we consider a generalisation of a class of Banach lattices introduced in Johansson (Syst Control Lett 57:105–111, 2008). We use Laplace transform methods to show that the norm of a convolution operator with symbol μ on such a space is bounded below by the L ∞ norm of the Fourier–Stieltjes transform of μ. We also show that for any Banach lattice of locally integrable functions on G with a shift-invariant norm, the norm of a convolution operator with symbol μ is bounded above by the total variation of μ." @default.
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- W2042118456 date "2010-07-17" @default.
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- W2042118456 title "Convolution Operators on Banach Lattices with Shift-Invariant Norms" @default.
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- W2042118456 doi "https://doi.org/10.1007/s00020-010-1817-4" @default.
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