carleson operator
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Author(s):  
Mikael Lindström ◽  
Mieczysław Mastyło ◽  
Paweł Mleczko ◽  
David Norrbo ◽  
Michał Rzeczkowski

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.


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

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

2012 ◽  
Vol 167 (3-4) ◽  
pp. 571-581 ◽  
Author(s):  
Elena Prestini ◽  
Silei Wang
Keyword(s):  

2006 ◽  
Vol 58 (1) ◽  
pp. 154-179 ◽  
Author(s):  
Elena Prestini

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.


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