Sparse bounds for maximal monomial oscillatory Hilbert transforms
نویسندگان
چکیده
منابع مشابه
Uniform 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...
متن کاملBilinear 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 کاملEndpoint Bounds for an Analytic Family of Hilbert Transforms
In R2, we consider an analytic family of operators Hz , z ∈ C, whose convolution kernel is obtained by taking −z − 1 derivatives of arclength measure on the parabola (t, t2) in a homogeneous way, defined in such a way so that H−1 be the standard parabolic Hilbert transform. For a fixed z, we study the set of p for which Hz is bounded on Lp(R2) and for the critical z that captures the degree of ...
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, Ii
We continue the investigation initiated in [8] of uniform L bounds for the family of bilinear Hilbert transforms Hα,β(f, g)(x) = p.v. ∫ R f(x − αt)g(x − βt) dt t . In this work we show that Hα,β map L1(R) × L2(R) into L(R) uniformly in the real parameters α, β satisfying | β − 1| ≥ c > 0 when 1 < p1, p2 < 2 and 2 3 < p = p1p2 p1+p2 < ∞. As a corollary we obtain L × L∞ → L uniform bounds in the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2018
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm8699-7-2017