scholarly journals Weak type estimates for some maximal operators on the weighted Hardy spaces

1995 ◽  
Vol 33 (2) ◽  
pp. 377-384 ◽  
Author(s):  
Shuichi Sato
Keyword(s):  
Hardy Spaces ◽  
Weak Type ◽  
Maximal Operators ◽  
Weighted Hardy Spaces ◽  
Weak Type Estimates

Weak type estimates for maximal operators with a cylindric distance function

2006 ◽  
Vol 253 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Sunggeum Hong ◽  
Paul Taylor ◽  
Chan Woo Yang
Keyword(s):  
Distance Function ◽  
Weak Type ◽  
Maximal Operators ◽  
Weak Type Estimates

scholarly journals BEST CONSTANTS IN THE WEAK-TYPE ESTIMATES FOR UNCENTERED MAXIMAL OPERATORS

2012 ◽  
Vol 54 (3) ◽  
pp. 655-663
Author(s):  
ADAM OSȨKOWSKI
Keyword(s):  
Maximal Operator ◽  
Borel Measure ◽  
Weak Type ◽  
Integrable Function ◽  
Maximal Operators ◽  
Weak Type Estimates ◽  
Locally Integrable Function ◽  
Image Position ◽  
Strong Maximal Operator ◽  
General Product

AbstractLet μ be a Borel measure on ℝ. The paper contains the proofs of the estimates and Here A is a subset of ℝ, f is a μ-locally integrable function, μ is the uncentred maximal operator with respect to μ and cp,q, and Cp,q are finite constants depending only on the parameters indicated. In the case when μ is the Lebesgue measure, the optimal choices for cp,q and Cp,q are determined. As an application, we present some related tight bounds for the strong maximal operator on ℝn with respect to a general product measure.

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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