Bilinear Hilbert transforms along curves, I: the monomial case
نویسندگان
چکیده
منابع مشابه
Bilinear Hilbert Transforms along Curves I. the Monomial Case
We establish an L2×L2 to L estimate for the bilinear Hilbert transform along a curve defined by a monomial. Our proof is closely related to multilinear oscillatory integrals.
متن کاملUniform Bounds for the Bilinear Hilbert Transforms, I
It is shown that the bilinear Hilbert transforms Hα,β(f, g)(x) = p.v. Z R f(x− αt)g(x− βt) dt t map L1(R)×L2(R)→ L(R) uniformly in the real parameters α, β when 2 < p1, p2 <∞ and 1 < p = p1p2 p1+p2 < 2. Combining this result with the main result in [9], it follows that the operators H1,α map L (R) × L∞(R) → L(R) uniformly in the real parameter α ∈ [0, 1], as conjectured by A. Calderón.
متن کاملUniform Bounds for the Bilinear Hilbert Transforms
It is shown that the bilinear Hilbert transforms Hα,β(f, g)(x) = p.v. ∫ R f(x− αt)g(x− βt) dt t map Lp1(R) × Lp2(R) → Lp(R) uniformly in the real parameters α, β when 2 < p1, p2 < ∞ and 1 < p = p1p2 p1+p2 < 2. Combining this result with the main result in [9], we deduce that the operators H1,α map L2(R)×L∞(R) → L2(R) uniformly in the real parameter α ∈ [0, 1]. This completes a program initiated...
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It is a conjecture due to M. E. Rossi that the Hilbert function of a one-dimensional Gorenstein local ring is non-decreasing. In this article, we show that the Hilbert function is non-decreasing for local Gorenstein rings with embedding dimension four associated to monomial curves, under some arithmetic assumptions on the generators of their defining ideals in the noncomplete intersection case....
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ژورنال
عنوان ژورنال: Analysis & PDE
سال: 2013
ISSN: 1948-206X,2157-5045
DOI: 10.2140/apde.2013.6.197