scholarly journals Weak type estimates of square functions associated with quasiradial Bochner–Riesz means on certain Hardy spaces

2008 ◽  
Vol 339 (1) ◽  
pp. 266-280 ◽  
Author(s):  
Yong-Cheol Kim
Keyword(s):  
Hardy Spaces ◽  
Weak Type ◽  
Square Functions ◽  
Riesz Means ◽  
Weak Type Estimates

Sublinear operators on weighted Hardy spaces with variable exponents

2019 ◽  
Vol 31 (3) ◽  
pp. 607-617 ◽  
Author(s):  
Kwok-Pun Ho
Keyword(s):  
Hardy Spaces ◽  
Variable Exponents ◽  
Square Functions ◽  
Weighted Hardy Spaces ◽  
Riesz Means ◽  
Marcinkiewicz Integrals ◽  
Sublinear Operators ◽  
Intrinsic Square Functions

Abstract We establish the mapping properties for some sublinear operators on weighted Hardy spaces with variable exponents by using extrapolation. In particular, we study the Calderón–Zygmund operators, the maximal Bochner–Riesz means, the intrinsic square functions and the Marcinkiewicz integrals on weighted Hardy spaces with variable exponents.

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 Weak Type Estimates of the Maximal Quasiradial Bochner-Riesz Operator On Certain Hardy Spaces

2003 ◽  
Vol 46 (2) ◽  
pp. 191-203 ◽  
Author(s):  
Yong-Cheol Kim
Keyword(s):  
Finite Type ◽  
Distance Function ◽  
Hardy Spaces ◽  
Infinitesimal Generator ◽  
Weak Type ◽  
Bounded Operator ◽  
Smooth Convex ◽  
Riesz Operator ◽  
Weak Type Estimates ◽  
Dilation Group

AbstractLet be the dilation group in generated by the infinitesimal generator M where At = exp(M log t), and let be a At-homogeneous distance function defined on . For , we define the maximal quasiradial Bochner-Riesz operator of index δ > 0 byIf At = tI and is a smooth convex hypersurface of finite type, then we prove in an extremely easy way that is well defined on Hp() when δ = n(1/p − 1/2) − 1/2 and 0 < p < 1; moreover, it is a bounded operator from Hp() into Lp,∞().If At = tI and , we also prove that is a bounded operator from Hp() into Lp() when δ > n(1/p − 1/2) − 1/2 and 0 < p < 1.

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