Criteria of strong type two-weighted inequalities for fractional maximal functions

1996 ◽  
Vol 3 (5) ◽  
pp. 423-446 ◽  
Author(s):  
A. Gogatishvili ◽  
V. Kokilashvili
Keyword(s):  
Maximal Functions ◽  
Weighted Inequalities ◽  
Strong Type

Criteria of Strong Type Two-Weighted Inequalities for Fractional Maximal Functions

1996 ◽  
Vol 3 (5) ◽  
pp. 423-446
Author(s):  
A. Gogatishvili ◽  
V. Kokilashvili
Keyword(s):  
Maximal Functions ◽  
Homogeneous Type ◽  
Weighted Inequalities ◽  
Strong Type ◽  
Weight Problem

Abstract A strong type two-weight problem is solved for fractional maximal functions defined in homogeneous type general spaces. A similar problem is also solved for one-sided fractional maximal functions.

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.

Weighted Inequalities for One-Sided Maximal Functions

1990 ◽  
Vol 319 (2) ◽  
pp. 517 ◽  
Author(s):  
F. J. Martin-Reyes ◽  
P. Ortega Salvador ◽  
A. De La Torre
Keyword(s):  
Maximal Functions ◽  
Weighted Inequalities

Weighted Inequalities for Hardy–Steklov Operators

2007 ◽  
Vol 59 (2) ◽  
pp. 276-295 ◽  
Author(s):  
A. L. Bernardis ◽  
F. J. Martín-Reyes ◽  
P. Ortega Salvador
Keyword(s):  
Weak Type ◽  
Type Inequality ◽  
Continuous Functions ◽  
Weighted Inequalities ◽  
Strong Type ◽  
Strong Type Inequality ◽  
Differentiability Properties

AbstractWe characterize the pairs of weights (v, w) for which the operator with s and h increasing and continuous functions is of strong type (p, q) or weak type (p, q) with respect to the pair (v, w) in the case 0 < q < p and 1 < p < ∞. The result for the weak type is new while the characterizations for the strong type improve the ones given by H. P. Heinig and G. Sinnamon. In particular, we do not assume differentiability properties on s and h and we obtain that the strong type inequality (p, q), q < p, is characterized by the fact that the functionbelongs to Lr(gqw), where 1/r = 1/q – 1/p and the supremum is taken over all c and d such that c ≤ x ≤ d and s(d) ≤ h(c).

scholarly journals MIXED NORM INEQUALITIES FOR SOME DIRECTIONAL MAXIMAL OPERATORS

2012 ◽  
Vol 86 (3) ◽  
pp. 448-455
Author(s):  
DAH-CHIN LUOR
Keyword(s):  
Harmonic Analysis ◽  
Maximal Functions ◽  
Maximal Operators ◽  
Mixed Norm ◽  
Weighted Inequalities ◽  
Norm Inequalities ◽  
One Dimensional

AbstractMixed norm inequalities for directional operators are closely related to the boundedness problems of several important operators in harmonic analysis. In this paper we prove weighted inequalities for some one-dimensional one-sided maximal functions. Then by applying these results, we establish mixed norm inequalities for directional maximal operators which are defined from these one-dimensional maximal functions. We also estimate the constants in these inequalities.

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