scholarly journals New characterizations and applications of inhomogeneous Besov and Triebel–Lizorkin spaces on homogeneous type spaces and fractals

2002 ◽  
Vol 403 ◽  
pp. 1-102 ◽  
Author(s):  
Yongsheng Han ◽  
Dachun Yang
Keyword(s):  
Homogeneous Type ◽  
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.

scholarly journals Some new Besov and Triebel-Lizorkin spaces associated with para-accretive functions on spaces of homogeneous type

2006 ◽  
Vol 80 (2) ◽  
pp. 229-262 ◽  
Author(s):  
Dongguo Deng ◽  
Dachun Yang
Keyword(s):  
Besov Space ◽  
Type Inequality ◽  
Space Of Homogeneous Type ◽  
Embedding Theorems ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Lizorkin Space ◽  
Hardy Type ◽  
Riesz Operators ◽  
Type Spaces

AbstractLet (X, ρ, μ)d, θ be a space of homogeneous type with d < 0 and θ ∈ (0, 1], b be a para-accretive function, ε ∈ (0, θ], ∣s∣ > ∈ and a0 ∈ (0, 1) be some constant depending on d, ∈ and s. The authors introduce the Besov space bBspq (X) with a0 > p ≧ ∞, and the Triebel-Lizorkin space bFspq (X) with a0 > p > ∞ and a0 > q ≧∞ by first establishing a Plancherel-Pôlya-type inequality. Moreover, the authors establish the frame and the Littlewood-Paley function characterizations of these spaces. Furthermore, the authors introduce the new Besov space b−1 Bs (X) and the Triebel-Lizorkin space b−1 Fspq (X). The relations among these spaces and the known Hardy-type spaces are presented. As applications, the authors also establish some real interpolation theorems, embedding theorems, T b theorems, and the lifting property by introducing some new Riesz operators of these spaces.

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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