On some singular integral operatorsclose to the Hilbert transform

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

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

Colloquium Mathematicae, Tome 72 (1997), p. 9-17 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $T_{m} f (x) = p . v . \int k (x - y) m (x + y) f (y) d y$ where $k (x) = \sum_{j \in ℤ} 2^{j} φ_{j} (2^{j} x)$ for a family of functions ${φ_{j}}_{j \in ℤ}$ satisfying conditions (1.1)-(1.3) given below.

Publié le : 1997-01-01

Zbl 0869.42003

EUDML-ID : urn:eudml:doc:210458

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     author = {T. Godoy and L. Saal and M. Urciuolo},
     title = {On some singular integral operatorsclose to the Hilbert transform},
     journal = {Colloquium Mathematicae},
     volume = {72},
     year = {1997},
     pages = {9-17},
     zbl = {0869.42003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv72i1p9bwm}
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Godoy, T.; Saal, L.; Urciuolo, M. On some singular integral operatorsclose to the Hilbert transform. Colloquium Mathematicae, Tome 72 (1997) pp. 9-17. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv72i1p9bwm/

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