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.

scholarly journals Criteria of General Weak Type Inequalities for Integral Transforms with Positive Kernels

1994 ◽  
Vol 1 (1) ◽  
pp. 9-29
Author(s):  
I. Genebashvili ◽  
A. Gogatishvili ◽  
V. Kokilashvili
Keyword(s):  
Weak Type ◽  
Sufficient Conditions ◽  
Nonnegative Function ◽  
Integral Transforms ◽  
Lorentz Spaces ◽  
Quasiconvex Functions ◽  
Homogeneous Type ◽  
Necessary And Sufficient ◽  
Positive Kernels ◽  
Homogeneous Type Space

Abstract Necessary and sufficient conditions are derived in order that an inequality of the form be fulfilled for some positive c independent of λ and a ν-measurable nonnegative function ƒ : X → R 1, where k : X × X × [0, ∞) → R 1 is a nonnegative measurable kernel, (X, d, μ) is a homogeneous type space, φη and ψ are quasiconvex functions, ψ ∈ Δ2, and t –α θ(t) is a decreasing function for some α, 0 < α < 1. A similar problem was solved in Lorentz spaces with weights.

Essential norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2877-2889 ◽  
Author(s):  
Amir Sanatpour ◽  
Mostafa Hassanlou
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Essential Norm ◽  
Necessary And Sufficient Conditions ◽  
Norm Estimates ◽  
Type Spaces ◽  
Necessary And Sufficient

We study boundedness of weighted differentiation composition operators Dk?,u between Zygmund type spaces Z? and Bloch type spaces ?. We also give essential norm estimates of such operators in different cases of k ? N and 0 < ?,? < ?. Applying our essential norm estimates, we get necessary and sufficient conditions for the compactness of these operators.

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