scholarly journals Atomic Decomposition of Weighted Lorentz Spaces and Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Eddy Kwessi ◽  
Geraldo de Souza ◽  
Fidele Ngwane ◽  
Asheber Abebe
Keyword(s):  
Atomic Decomposition ◽  
Composition Operators ◽  
Lorentz Spaces ◽  
Weighted Lorentz Spaces

We obtain an atomic decomposition of weighted Lorentz spaces for a class of weights satisfying the Δ2condition. Consequently, we study operators such as the multiplication and composition operators and also provide Hölder’s-type and duality-Riesz type inequalities on these weighted Lorentz spaces.

scholarly journals Compactness and essential norms of composition operators on Orlicz–Lorentz spaces

2012 ◽  
Vol 25 (11) ◽  
pp. 1778-1783 ◽  
Author(s):  
Yunan Cui ◽  
Henryk Hudzik ◽  
Rajeev Kumar ◽  
Romesh Kumar
Keyword(s):  
Composition Operators ◽  
Lorentz Spaces

Boundedness and compactness of Hardy-type integral operators on Lorentz-type spaces

2018 ◽  
Vol 30 (4) ◽  
pp. 997-1011 ◽  
Author(s):  
Hongliang Li ◽  
Qinxiu Sun ◽  
Xiao Yu
Keyword(s):  
Banach Spaces ◽  
Measurable Function ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Lorentz Spaces ◽  
Orlicz Functions ◽  
Hardy Type ◽  
Type Integral ◽  
Type Spaces ◽  
Weighted Lorentz Spaces

Abstract Given measurable functions ϕ, ψ on {\mathbb{R}^{+}} and a kernel function {k(x,y)\geq 0} satisfying the Oinarov condition, we study the Hardy operator Kf(x)=\psi(x)\int_{0}^{x}k(x,y)\phi(y)f(y)\,dy,\quad x>0, between Orlicz–Lorentz spaces {\Lambda_{X}^{G}(w)} , where f is a measurable function on {\mathbb{R}^{+}} . We obtain sufficient conditions of boundedness of {K:\Lambda_{u_{0}}^{G_{0}}(w_{0})\rightarrow\Lambda_{u_{1}}^{G_{1}}(w_{1})} and {K:\Lambda_{u_{0}}^{G_{0}}(w_{0})\rightarrow\Lambda_{u_{1}}^{G_{1},\infty}(w_{% 1})} . We also look into boundedness and compactness of {K:\Lambda_{u_{0}}^{p_{0}}(w_{0})\rightarrow\Lambda_{u_{1}}^{p_{1},q_{1}}(w_{1% })} between weighted Lorentz spaces. The function spaces considered here are quasi-Banach spaces rather than Banach spaces. Specializing the weights and the Orlicz functions, we restore the existing results as well as we achieve new results in the new and old settings.

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