scholarly journals Borderline weak-type estimates for singular integrals and square functions

2015 ◽  
Vol 48 (1) ◽  
pp. 63-73 ◽  
Author(s):  
Carlos Domingo-Salazar ◽  
Michael Lacey ◽  
Guillermo Rey
Keyword(s):  
Singular Integrals ◽  
Weak Type ◽  
Square Functions ◽  
Weak Type Estimates

scholarly journals On a counterexample related to weighted weak type estimates for singular integrals

2017 ◽  
Vol 145 (7) ◽  
pp. 3005-3012 ◽  
Author(s):  
Marcela Caldarelli ◽  
Andrei K. Lerner ◽  
Sheldy Ombrosi
Keyword(s):  
Singular Integrals ◽  
Weak Type ◽  
Weak Type Estimates

scholarly journals Weak type estimates for functions of Marcinkiewicz type with fractional integrals of mixed homogeneity

2019 ◽  
Vol 125 (1) ◽  
pp. 135-162
Author(s):  
Shuichi Sato
Keyword(s):  
Weak Type ◽  
Fractional Integrals ◽  
Square Functions ◽  
Riesz Potentials ◽  
Type Estimate ◽  
Weak Type Estimates

We prove the endpoint weak type estimate for square functions of Marcinkiewicz type with fractional integrals associated with non-isotropic dilations. This generalizes a result of C. Fefferman on functions of Marcinkiewicz type by considering fractional integrals of mixed homogeneity in place of the Riesz potentials of Euclidean structure.

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