Geodesic
On some singular integral operatorsclose to the Hilbert transform
Colloquium Mathematicum, Tome 72 (1997) no. 1, pp. 9-17.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let m: ℝ → ℝ be a function of bounded variation. We prove the $L^p(ℝ)$-boundedness, 1 p ∞, of the one-dimensional integral operator defined by $T_m f(x) = p.v. \int k(x-y) m(x+y) f(y)dy$ where $k(x) = \sum_{j ∈ ℤ} 2^j φ _j (2^j x)$ for a family of functions ${φ_j}_{j∈ℤ}$ satisfying conditions (1.1)-(1.3) given below.
DOI : 10.4064/cm-72-1-9-17

T. Godoy 1 ; L. Saal 1 ; M. Urciuolo 1

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T. Godoy; L. Saal; M. Urciuolo. On some singular integral operatorsclose to the Hilbert transform. Colloquium Mathematicum, Tome 72 (1997) no. 1, pp. 9-17. doi : 10.4064/cm-72-1-9-17. http://geodesic.mathdoc.fr/articles/10.4064/cm-72-1-9-17/

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