scholarly journals A Fefferman–Stein inequality for the Carleson operator

2018 ◽  
Vol 34 (1) ◽  
pp. 221-244 ◽  
Author(s):  
David Beltran
Keyword(s):  
Carleson Operator

CARLESON INTERPOLATING SEQUENCES FOR BANACH SPACES OF ANALYTIC FUNCTIONS

2021 ◽  
pp. 1-31
Author(s):  
Mikael Lindström ◽  
Mieczysław Mastyło ◽  
Paweł Mleczko ◽  
David Norrbo ◽  
Michał Rzeczkowski
Keyword(s):  
Banach Spaces ◽  
Hardy Spaces ◽  
Orlicz Spaces ◽  
Interpolation Spaces ◽  
Interpolation Theory ◽  
Interpolating Sequences ◽  
Uniformly Separated ◽  
Carleson Operator ◽  
Spaces Of Analytic Functions ◽  
By Products

Abstract This paper presents an approach, based on interpolation theory of operators, to the study of interpolating sequences for interpolation Banach spaces between Hardy spaces. It is shown that the famous Carleson result for H ∞ can be lifted to a large class of abstract Hardy spaces. A description is provided of the range of the Carleson operator defined on interpolation spaces between the classical Hardy spaces in terms of uniformly separated sequences. A key role in this description is played by some general interpolation results proved in the paper. As by-products, novel results are obtained which extend the Shapiro–Shields result on the characterisation of interpolation sequences for the classical Hardy spaces H p . Applications to Hardy–Lorentz, Hardy–Marcinkiewicz and Hardy–Orlicz spaces are presented.

A littlewood-paley inequality for the Carleson operator

2000 ◽  
Vol 6 (5) ◽  
pp. 457-466 ◽  
Author(s):  
Elena Prestini ◽  
Per Sjölin
Keyword(s):  
Carleson Operator

Singular Integrals on Product Spaces Related to the Carleson Operator

2006 ◽  
Vol 58 (1) ◽  
pp. 154-179 ◽  
Author(s):  
Elena Prestini
Keyword(s):  
Fourier Series ◽  
Hilbert Transform ◽  
Singular Integrals ◽  
Double Fourier Series ◽  
Variable Coefficients ◽  
Product Spaces ◽  
One Dimensional ◽  
Carleson Operator ◽  
Two Phases ◽  
The Hilbert Transform

AbstractWe prove Lp(T2) boundedness, 1 < p ≤ 2, of variable coefficients singular integrals that generalize the double Hilbert transform and present two phases that may be of very rough nature. These operators are involved in problems of a.e. convergence of double Fourier series, likely in the role played by the Hilbert transform in the proofs of a.e. convergence of one dimensional Fourier series. The proof due to C.Fefferman provides a basis for our method.

scholarly journals The Polynomial Carleson operator

2020 ◽  
Vol 192 (1) ◽  
pp. 47
Author(s):  
Lie
Keyword(s):  
Carleson Operator

scholarly journals A polynomial Carleson operator along the paraboloid

2019 ◽  
Vol 35 (2) ◽  
pp. 339-422 ◽  
Author(s):  
Lillian Pierce ◽  
Po-Lam Yung
Keyword(s):  
Carleson Operator

A Discrete Model for the Bi-Carleson Operator

2002 ◽  
Vol 12 (6) ◽  
pp. 1324-1364 ◽  
Author(s):  
C. Muscalu ◽  
T. Tao ◽  
C. Thiele
Keyword(s):  
Discrete Model ◽  
Carleson Operator
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