Abstract
The integral convolution operator in ℝn
is well defined and bounded in L p(ℝn), 1≤p ≤ ∞, as k∈ L l(ℝn). However, operators very similar to (0.1), but having a non-integrable kernel, appear quite frequently in applications. The Hilbert transform on the real line l is a typical example.
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Dyn’kin, E.M. (1991). Methods of the Theory of Singular Integrals: Hilbert Transform and Calderón-Zygmund Theory. In: Khavin, V.P., Nikol’skij, N.K. (eds) Commutative Harmonic Analysis I. Encyclopaedia of Mathematical Sciences, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02732-5_3
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