Criteria of a multi-weight weak type inequality in Orlicz classes for maximal functions defined on homogeneous type spaces

2020 ◽  
Vol 162 (2) ◽  
pp. 677-689
Author(s):  
S. Ding ◽  
Y. Ren
Keyword(s):  
Weak Type ◽  
Type Inequality ◽  
Maximal Functions ◽  
Homogeneous Type ◽  
Weak Type Inequality ◽  
Type Spaces ◽  
Homogeneous Type Spaces

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.

Necessary and Sufficient Conditions for Weighted Orlicz Class Inequalities for Maximal Functions and Singular Integrals. II

1995 ◽  
Vol 2 (5) ◽  
pp. 445-468
Author(s):  
A. Gogatishvili ◽  
V. Kokilashvili
Keyword(s):  
Singular Integrals ◽  
Sufficient Conditions ◽  
Maximal Functions ◽  
Necessary And Sufficient Conditions ◽  
Homogeneous Type ◽  
Orlicz Class ◽  
Weight Problems ◽  
Type Spaces ◽  
Necessary And Sufficient ◽  
Homogeneous Type Spaces

Abstract This paper continues the investigation of weight problems in Orlicz classes for maximal functions and singular integrals defined on homogeneous type spaces considered in [Gogatishvili and Kokilashvili, Georguian Math. J. 2: 361–384, 1995].

Necessary and Sufficient Conditions for Weighted Orlicz Class Inequalities for Maximal Functions and Singular Integrals. I

1995 ◽  
Vol 2 (4) ◽  
pp. 361-384
Author(s):  
A. Gogatishvili ◽  
V. Kokilashvili
Keyword(s):  
Singular Integrals ◽  
Sufficient Conditions ◽  
Maximal Functions ◽  
Homogeneous Type ◽  
Weighted Inequalities ◽  
Strong Type ◽  
Orlicz Class ◽  
Type Spaces ◽  
Necessary And Sufficient ◽  
Homogeneous Type Spaces

Abstract Criteria of various weak and strong type weighted inequalities are established for singular integrals and maximal functions defined on homogeneous type spaces in the Orlicz classes.

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.

Sign in / Sign up

Export Citation Format

Share Document