Singular integrals with highly oscillating kernels on product spaces

ArticleOriginal scientific text

Title

Authors ¹

Dipartimento di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma, Italy

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.

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