We prove the boundedness from L-p(T-2) to itself, 1 < p < infinity, 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 vertical bar y'vertical bar > vertical bar x'vertical bar, and presenting phases lambda(Ax+By) with 0 <= A, B <= 1 and lambda >= 0. The norms of these oscillatory singular integrals are proved to be independent of all parameters A, B and lambda 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.

Prestini, E. (2006). Singular integrals with bilinear phases, 22(1), 251-260 [10.1007/s10114-005-0562-0].

Singular integrals with bilinear phases

PRESTINI, ELENA
2006-01-01

Abstract

We prove the boundedness from L-p(T-2) to itself, 1 < p < infinity, 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 vertical bar y'vertical bar > vertical bar x'vertical bar, and presenting phases lambda(Ax+By) with 0 <= A, B <= 1 and lambda >= 0. The norms of these oscillatory singular integrals are proved to be independent of all parameters A, B and lambda 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.
2006
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
English
Hardy-Littlewood maximal function; maximal Hilbert transform; maximal Carleson operator; oscillatory singular integrals; a. e. convergence of double Fourier series
Prestini, E. (2006). Singular integrals with bilinear phases, 22(1), 251-260 [10.1007/s10114-005-0562-0].
Prestini, E
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/38924
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