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The class of convolution operators on the Marcinkiewicz spaces

Ka-Sing Lau (1981)

Annales de l'institut Fourier

Let 𝒯 X denote the operator-norm closure of the class of convolution operators Φ μ : X X where X is a suitable function space on R . Let r p be the closed subspace of regular functions in the Marinkiewicz space p , 1 p < . We show that the space 𝒯 r p is isometrically isomorphic to 𝒯 L p and that strong operator sequential convergence and norm convergence in 𝒯 r p coincide. We also obtain some results concerning convolution operators under the Wiener transformation. These are to improve a Tauberian theorem of Wiener on 2 .

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