scholarly journals Criteria of weighted inequalities in Orlicz classes for maximal functions defined on homogeneous type spaces

1994 ◽  
Vol 1 (6) ◽  
pp. 641-673 ◽  
Author(s):  
A. Gogatishvili ◽  
V. Kokilashvili
Keyword(s):  
Maximal Functions ◽  
Homogeneous Type ◽  
Weighted Inequalities ◽  
Type Spaces ◽  
Homogeneous Type Spaces

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 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].

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.

scholarly journals Non-smooth atomic decomposition of variable 2-microlocal Besov-type and Triebel–Lizorkin-type spaces

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Helena F. Gonçalves
Keyword(s):  
Atomic Decomposition ◽  
Morrey Spaces ◽  
Maximal Functions ◽  
Variable Exponents ◽  
Atomic Decompositions ◽  
Local Means ◽  
Essential Tool ◽  
Pointwise Multipliers ◽  
Type Spaces

AbstractIn this paper we provide non-smooth atomic decompositions of 2-microlocal Besov-type and Triebel–Lizorkin-type spaces with variable exponents $$B^{\varvec{w}, \phi }_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ B p ( · ) , q ( · ) w , ϕ ( R n ) and $$F^{\varvec{w}, \phi }_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ F p ( · ) , q ( · ) w , ϕ ( R n ) . Of big importance in general, and an essential tool here, are the characterizations of the spaces via maximal functions and local means, that we also present. These spaces were recently introduced by Wu et al. and cover not only variable 2-microlocal Besov and Triebel–Lizorkin spaces $$B^{\varvec{w}}_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ B p ( · ) , q ( · ) w ( R n ) and $$F^{\varvec{w}}_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ F p ( · ) , q ( · ) w ( R n ) , but also the more classical smoothness Morrey spaces $$B^{s, \tau }_{p,q}({\mathbb {R}}^n)$$ B p , q s , τ ( R n ) and $$F^{s,\tau }_{p,q}({\mathbb {R}}^n)$$ F p , q s , τ ( R n ) . Afterwards, we state a pointwise multipliers assertion for this scale.

Sign in / Sign up

Export Citation Format

Share Document