Singular integrals with highly oscillating kernels on product spaces

Prestini, Elena

Prestini, Elena

Colloquium Mathematicae, Tome 84/85 (2000), p. 9-13 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove the $L^{2} (^{2})$ boundedness of the oscillatory singular integrals $P_{0} f (x, y) = \int_{D_{x}} e^{i (M_{2} (x) y^{'} + M_{1} (x) x^{'})} ο v e r x^{'} y^{'} f (x - x^{'}, y - y^{'}) d x^{'} d y^{'}$ for arbitrary real-valued $L^{\infty}$ functions $M_{1} (x), M_{2} (x)$ and for rather general domains $D_{x} \subseteq^{2}$ whose dependence upon x satisfies no regularity assumptions.

Publié le : 2000-01-01

Zbl 0969.32007

EUDML-ID : urn:eudml:doc:210844

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     author = {Elena Prestini},
     title = {Singular integrals with highly oscillating kernels on product spaces},
     journal = {Colloquium Mathematicae},
     volume = {84/85},
     year = {2000},
     pages = {9-13},
     zbl = {0969.32007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv86i1p9bwm}
}

Prestini, Elena. Singular integrals with highly oscillating kernels on product spaces. Colloquium Mathematicae, Tome 84/85 (2000) pp. 9-13. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv86i1p9bwm/

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