Harmonic analysis, Carleson theorems, and multilinear analysis

نویسندگان

  • Michael Lacey
  • Christoph Thiele
چکیده

We outline a method for controlling a model for the return times operator. For more information about how this model operator relates to the return times theorem, see the summary by Patrick LaVictoire in these conference proceedings. 1.1 Notation and prior results For a sequence (xj)j ⊆ C, define ||xj ||Ṽ r k = sup M,k0,...,kM ( M ∑ m=1 |xkm − xkm−1 | ) 1 r

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Generalizations of the Carleson-hunt Theorem I. the Classical Singularity Case

In this article, we prove L estimates for a general maximal operator, which extend both the classical Coifman-Meyer [2] and Carleson-Hunt [1], [7] theorems in harmonic analysis.

متن کامل

[ m at h . C A ] 1 0 Ju n 20 02 CARLESON MEASURES , TREES , EXTRAPOLATION , AND T ( b ) THEOREMS

The theory of Carleson measures, stopping time arguments, and atomic decompositions has been well-established in harmonic analysis. More recent is the theory of phase space analysis from the point of view of wave packets on tiles, tree selection algorithms, and tree size estimates. The purpose of this paper is to demonstrate that the two theories are in fact closely related, by taking existing ...

متن کامل

Carleson Measures Associated with Families of Multilinear Operators

Abstract. In this work we investigate the construction of Carleson measures from families of multilinear integral operators applied to tuples of L∞ and BMO functions. We show that if the family Rt of multilinear operators possesses cancellation in each variable, then for BMO functions b1, . . . , bm, the measure |Rt(b1, . . . , bm)(x)|dxdt/t is Carleson. However, if the family of multilinear op...

متن کامل

L Theory for Outer Measures and Two Themes of Lennart Carleson United

Abstract. We develop a theory of Lp spaces based on outer measures generated through coverings by distinguished sets. The theory includes as a special case the classical Lp theory on Euclidean spaces as well as some previously considered generalizations. The theory is a framework to describe aspects of singular integral theory, such as Carleson embedding theorems, paraproduct estimates, and T (...

متن کامل

Methods of Harmonic Analysis

I spent most of my research time this summer studying the basic methods of harmonic analysis. My goal was to write an explanation and elaboration of Fefferman’s 1973 paper, Pointwise Convergence of Fourier Series. I was attempting to fill in the details and clarify things to the degree that the paper would be accessible at the level of a beginning graduate student, and to add enough background ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009