The complete (L-P, L-P) mapping properties of some oscillatory integrals in several dimensions

Authors
Sampson, G Szeptycki, P
Citation
G. Sampson et P. Szeptycki, The complete (L-P, L-P) mapping properties of some oscillatory integrals in several dimensions, CAN J MATH, 53(5), 2001, pp. 1031-1056
Citations number
11
Categorie Soggetti
Mathematics
Journal title
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
ISSN journal
0008414X → ACNP
Volume
53
Issue
5
Year of publication
2001
Pages
1031 - 1056
Database
ISI
SICI code
0008-414X(200110)53:5<1031:TC(LMP>2.0.ZU;2-2
Abstract
We prove that the operators integral (R42) e(ixa.yb) phi (x, y) f(y) dy map L-p(R-2) into itself for p is an element of J = [aj + bj/aj+(bjr/2), aj+bj /aj(1 - r/2)] if a(l), b(l) greater than or equal to 1 and phi (x, y) = \x - y \ (-r), 0 less than or equal to r < 2, the result is sharp. Generalizat ions to dimensions d > 2 are indicated.