A weak type inequality for generalized maximal operators on spaces of homogeneous type

1999 ◽  
Vol 25 (1) ◽  
pp. 179-186 ◽  
Author(s):  
Byung-Oh Park ◽  
Бун-О Парк
Keyword(s):  
Weak Type ◽  
Type Inequality ◽  
Maximal Operators ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Weak Type Inequality

A Unified Version of Weighted Weak Type Inequality for Martingale Maximal Operators

2021 ◽  
Vol 58 (2) ◽  
pp. 216-229
Author(s):  
Yanbo Ren ◽  
Congbian Ma
Keyword(s):  
Weak Type ◽  
Type Inequality ◽  
Maximal Inequality ◽  
Complete Characterization ◽  
Maximal Operators ◽  
Weak Type Inequality

Let ɣ and Φ1 be nondecreasing and nonnegative functions defined on [0, ∞), and Φ2 is an N -function, u, v and w are weights. A unified version of weighted weak type inequality of the formfor martingale maximal operators f ∗ is considered, some necessary and su@cient conditions for it to hold are shown. In addition, we give a complete characterization of three-weight weak type maximal inequality of martingales. Our results generalize some known results on weighted theory of martingale maximal operators.

scholarly journals Commutators of the Hardy-Littlewood Maximal Operator with BMO Symbols on Spaces of Homogeneous Type

2008 ◽  
Vol 2008 ◽  
pp. 1-21 ◽  
Author(s):  
Guoen Hu ◽  
Haibo Lin ◽  
Dachun Yang
Keyword(s):  
Singular Integral ◽  
Maximal Operator ◽  
Weak Type ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Maximal Operators ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Littlewood Maximal Operator

WeightedLpforp∈(1,∞)and weak-type endpoint estimates with general weights are established for commutators of the Hardy-Littlewood maximal operator with BMO symbols on spaces of homogeneous type. As an application, a weighted weak-type endpoint estimate is proved for maximal operators associated with commutators of singular integral operators with BMO symbols on spaces of homogeneous type. All results with no weight on spaces of homogeneous type are also new.

Weighted Reverse Weak Type Inequality for General Maximal Functions

1995 ◽  
Vol 2 (3) ◽  
pp. 277-290
Author(s):  
J. Genebashvili
Keyword(s):  
Weak Type ◽  
Sufficient Conditions ◽  
Type Inequality ◽  
Maximal Functions ◽  
Homogeneous Type ◽  
Reverse Inequality ◽  
Weak Type Inequality ◽  
Type Spaces ◽  
Necessary And Sufficient ◽  
Homogeneous Type Spaces

Abstract Necessary and sufficient conditions are found to be imposed on a pair of weights, for which a weak type two-weighted reverse inequality holds, in the case of general maximal functions defined in homogeneous type spaces.

A weak-type (∞,∞) inequality for the triangular projection

2021 ◽  
Vol 612 ◽  
pp. 112-127
Author(s):  
Tomasz Gałązka ◽  
Adam Osękowski ◽  
Yahui Zuo
Keyword(s):  
Weak Type ◽  
Type Inequality ◽  
Weak Type Inequality

A note on the one-dimensional maximal function

1989 ◽  
Vol 111 (3-4) ◽  
pp. 325-328 ◽  
Author(s):  
Antonio Bernal
Keyword(s):  
Maximal Function ◽  
Weak Type ◽  
Type Inequality ◽  
Best Constant ◽  
Weak Type Inequality ◽  
One Dimensional ◽  
Littlewood Maximal Function ◽  
The One

SynopsisIn this note, we consider the Hardy-Littlewood maximal function on R for arbitrary measures, as was done by Peter Sjögren in a previous paper. We determine the best constant for the weak type inequality.

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