Singular Integrals with Bilinear Phases |
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Authors: | Elena Prestini |
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Institution: | (1) Dipartimento di Matematica, Università di Roma "Tor Vergata", Roma 00133, Italy |
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Abstract: | We prove the boundedness from L
p
(T
2) to itself, 1 < p < ∞, of highly oscillatory
singular integrals Sf(x, y) presenting singularities of the kind of the double Hilbert transform on a
non–rectangular domain of integration, roughly speaking, defined by |y'| > |x'|, and presenting phases
λ(Ax+By) with 0 ≤ A, B ≤ 1 and λ ≥ 0. The norms of these oscillatory singular integrals are proved
to be independent of all parameters A, B and λ involved. Our method extends to a more general family
of phases. These results are relevant to problems of almost everywhere convergence of double Fourier
and Walsh series.
Supported by Progetto cofimansiato HIUR "Amatisi Armomica" |
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Keywords: | Hardy-Littlewood maximal function Maximal Hilbert transform Maximal Carleson operator Oscillatory singular integrals a e convergence of double Fourier series |
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