Two-weight weak-type maximal inequalities for martingales

2009 ◽  
Vol 29 (2) ◽  
pp. 402-408 ◽  
Author(s):  
Ren Yanbo ◽  
Hou Youliang
Keyword(s):  
Weak Type ◽  
Maximal Inequalities

scholarly journals A note on weighted maximal inequalities

1997 ◽  
Vol 40 (1) ◽  
pp. 193-205
Author(s):  
Qinsheng Lai
Keyword(s):  
Maximal Operator ◽  
Weak Type ◽  
Strong Type ◽  
Maximal Inequalities ◽  
Littlewood Maximal Operator

In this paper, we obtain some characterizations for the weighted weak type (1, q) inequality to hold for the Hardy-Littlewood maximal operator in the case 0<q<1; prove that there is no nontrivial weight satisfying one-weight weak type (p, q) inequalities when 0<p≠q< ∞, and discuss the equivalence between the weak type (p, q) inequality and the strong type (p, q) inequality when p≠q.

TRANSFERENCE OF WEAK TYPE MAXIMAL INEQUALITIES BY DISTRIBUTIONALLY BOUNDED REPRESENTATIONS

1992 ◽  
Vol 43 (3) ◽  
pp. 259-282 ◽  
Author(s):  
NAKHLÉ ASMAR ◽  
EARL BERKSON ◽  
T. A. GILLESPIE
Keyword(s):  
Weak Type ◽  
Maximal Inequalities

Maximal Inequalities of Weak Type

1966 ◽  
Vol 84 (2) ◽  
pp. 157 ◽  
Author(s):  
S. Sawyer
Keyword(s):  
Weak Type ◽  
Maximal Inequalities

Two-parameter strong laws and maximal inequalities for U-statistics

1987 ◽  
Vol 107 (1-2) ◽  
pp. 133-151 ◽  
Author(s):  
Terry R. McConnell
Keyword(s):  
Law Of Large Numbers ◽  
Weak Type ◽  
Sufficient Conditions ◽  
Strong Law ◽  
Strong Laws ◽  
Maximal Inequalities ◽  
U Statistics ◽  
Large Numbers ◽  
Necessary And Sufficient ◽  
Two Parameter

SynopsisWe provide necessary and sufficient conditions for two-parameter convergence in the strong law of large numbers for U-statistics. We also obtain weak-type (1,1) inequalities for one and two-sample U-statistics of order 2 which are, in a sense, best possible.

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