On the boundedness of classical operators on weighted lorentz spaces

1998 ◽  
Vol 5 (2) ◽  
pp. 177-200 ◽  
Author(s):  
Y. Rakotondratsimba
Keyword(s):  
Lorentz Spaces ◽  
Weighted Lorentz Spaces

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.

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.

SHARP CONSTANTS BETWEEN EQUIVALENT NORMS IN WEIGHTED LORENTZ SPACES

2010 ◽  
Vol 88 (1) ◽  
pp. 19-27 ◽  
Author(s):  
SORINA BARZA ◽  
JAVIER SORIA
Keyword(s):  
Lorentz Space ◽  
Lorentz Spaces ◽  
Best Constants ◽  
Sharp Constants ◽  
Dual Norm ◽  
Equivalent Norms ◽  
Weighted Lorentz Spaces ◽  
Weighted Lorentz Space

AbstractFor an increasing weight w in Bp (or equivalently in Ap), we find the best constants for the inequalities relating the standard norm in the weighted Lorentz space Λp(w) and the dual norm.

scholarly journals Calderón–Zygmund Operators and Commutators on Weighted Lorentz Spaces

2020 ◽  
Author(s):  
María J. Carro ◽  
Hongliang Li ◽  
Javier Soria ◽  
Qinxiu Sun
Keyword(s):  
Lorentz Spaces ◽  
Weighted Lorentz Spaces
Sign in / Sign up

Export Citation Format

Share Document