scholarly journals Sharp variation-norm estimates for oscillatory integrals related to Carleson’s theorem

2020 ◽  
Vol 13 (5) ◽  
pp. 1457-1500
Author(s):  
Shaoming Guo ◽  
Joris Roos ◽  
Po-Lam Yung
Keyword(s):  
Oscillatory Integrals ◽  
Norm Estimates ◽  
Sharp Variation ◽  
Variation Norm ◽  
Carleson’S Theorem

scholarly journals Estimates for Compositions of Maximal Operators with Singular Integrals

2013 ◽  
Vol 56 (4) ◽  
pp. 801-813 ◽  
Author(s):  
Richard Oberlin
Keyword(s):  
Singular Integrals ◽  
Weak Type ◽  
Operator Norm ◽  
Maximal Operators ◽  
Multiplier Operator ◽  
Norm Estimates ◽  
Variation Norm

Abstract.We prove weak-type (1, 1) estimates for compositions of maximal operators with singular integrals. Our main object of interest is the operator Δ*Ψ where Δ* is Bourgain’s maximal multiplier operator and is the sum of several modulated singular integrals; here our method yields a significantly improved bound for the Lq operator norm when 1 < q < 2. We also consider associated variation-norm estimates.

scholarly journals Oscillatory integrals related to Carleson’s theorem

2001 ◽  
Vol 8 (6) ◽  
pp. 789-800 ◽  
Author(s):  
Elias M. Stein ◽  
Stephen Wainger
Keyword(s):  
Oscillatory Integrals ◽  
Carleson’S Theorem

Essential norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2877-2889 ◽  
Author(s):  
Amir Sanatpour ◽  
Mostafa Hassanlou
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Essential Norm ◽  
Necessary And Sufficient Conditions ◽  
Norm Estimates ◽  
Type Spaces ◽  
Necessary And Sufficient

We study boundedness of weighted differentiation composition operators Dk?,u between Zygmund type spaces Z? and Bloch type spaces ?. We also give essential norm estimates of such operators in different cases of k ? N and 0 < ?,? < ?. Applying our essential norm estimates, we get necessary and sufficient conditions for the compactness of these operators.

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