A Vector-valued Weak Type Inequality for Ergodic Square Function

2018 ◽  
Vol 9 (5) ◽  
pp. 318-324
Author(s):  
Sakin Demir
Keyword(s):  
Weak Type ◽  
Type Inequality ◽  
Square Function ◽  
Weak Type Inequality ◽  
Vector Valued

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.

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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