منابع مشابه
Distributional Estimates for the Bilinear Hilbert Transform
We obtain size estimates for the distribution function of the bilinear Hilbert transform acting on a pair of characteristic functions of sets of finite measure, that yield exponential decay at infinity and blowup near zero to the power −2/3 (modulo some logarithmic factors). These results yield all known L bounds for the bilinear Hilbert transform and provide new restricted weak type endpoint e...
متن کاملL(p) estimates for the bilinear Hilbert transform.
For the bilinear Hilbert transform given by: H fg(x) = p.v.integral f(x - y)g(x + y) dyy, we announce the inequality parallel H fg parallel (p(3) ) </= K(p(1) ) (,p(2) ) parallel f parallel (p(1) ) parallel g parallel (p(2) ), provided 2 < p(1), p(2) < infinity, 1/p(3) = 1/p(1) + 1/p(2) and 1 < p(3) < 2.
متن کاملWeighted Estimates for the Hilbert Transform of Odd Functions
The aim of the present paper is to characterize the classes of weights which ensure the validity of one-weighted strong, weak or extra-weak type estimates in Orlicz classes for the integral operator H0f(x) = 2 π ∫ ∞ 0 yf(y) x2 − y2 dy, x ∈ (0,∞).
متن کاملWiener-wintner for Hilbert Transform
We prove the following extension of the Wiener–Wintner Theorem and the Carleson Theorem on pointwise convergence of Fourier series: For all measure preserving flows (X,μ, Tt) and f ∈ L(X,μ), there is a set Xf ⊂ X of probability one, so that for all x ∈ Xf we have lim s↓0 ∫ s<|t|<1/s e f(Tt x) dt t exists for all θ. The proof is by way of establishing an appropriate oscillation inequality which ...
متن کاملA New Way of Looking at Distributional Estimates; Applications for the Bilinear Hilbert Transform
Distributional estimates for the Carleson operator acting on characteristic functions of measurable sets of finite measure were obtained by Hunt [12]. In this article we describe a simple method that yields such estimates for general operators acting on one or more functions. As an application we discuss how distributional estimates are obtained for the linear and bilinear Hilbert transform. Th...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1972
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-44-1-1-15