On Stein’s Conjecture on the Polynomial Carleson Operator
نویسنده
چکیده
We prove that the generalized Carleson operator Cd with polynomial phase function is of strong type (p, r), 1 < r < p < ∞; this yields a positive answer in the 1 < p < 2 case to a conjecture of Stein which asserts that for 1 < p < ∞ we have that Cd is of strong type (p, p). A key ingredient in this proof is the further extension of the relational time-frequency perspective (introduced in [5]) to the general polynomial phase.
منابع مشابه
The (weak-l2) Boundedness of the Quadratic Carleson Operator
We prove that the generalized Carleson operator with polynomial phase function of degree two is of weak type (2,2). For this, we introduce a new approach to the time-frequency analysis of the quadratic phase.
متن کاملOn some generalisations of Brown's conjecture
Let $P$ be a complex polynomial of the form $P(z)=zdisplaystyleprod_{k=1}^{n-1}(z-z_{k})$,where $|z_k|ge 1,1le kle n-1$ then $ P^prime(z)ne 0$. If $|z|
متن کاملA New Twist on the Carleson Operator
Must the Fourier series of an L function converge pointwise almost everywhere? In the 1960’s, Carleson answered this question in the affirmative, by studying a particular type of maximal singular integral operator, which has since become known as a Carleson operator. In the past 40 years, a number of important results have been proved for generalizations of the original Carleson operator. In th...
متن کاملOn the Bi-carleson Operator I. the Walsh Case
We prove L estimates for the Walsh model of the maximal bi-Carleson operator defined below. The corresponding estimates for the Fourier model will be obtained in the sequel [20] of this paper.
متن کاملThe Bi-carleson Operator
We prove L estimates (Theorem 1.3) for the Bi-Carleson operator defined below. The methods used are essentially based on the treatment of the Walsh analogue of the operator in the prequel [11] of this paper, but with additional technicalities due to the fact that in the Fourier model one cannot obtain perfect localization in both space and frequency.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008