On the trigonometric approximation of functions in weighted Lorentz spaces using Cesáro submethod

2018 ◽  
Vol 48 (2) ◽  
pp. 41-55
Author(s):  
Ahmet Hamdi Avsar ◽  
Yunus Emre Yildirir
Keyword(s):  
Lorentz Spaces ◽  
Trigonometric Approximation ◽  
Approximation Of Functions ◽  
Weighted Lorentz Spaces

scholarly journals Trigonometric approximation of functions $f(x,y)$ of generalized Lipschitz class by double Hausdorff matrix summability method

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abhishek Mishra ◽  
Vishnu Narayan Mishra ◽  
M. Mursaleen
Keyword(s):  
Double Fourier Series ◽  
Degree Of Approximation ◽  
Trigonometric Approximation ◽  
Lipschitz Class ◽  
Gamma Delta ◽  
Approximation Of Functions ◽  
Matrix Summability ◽  
Alpha Beta ◽  
Generalized Lipschitz Class ◽  
Hausdorff Matrix

AbstractIn this paper, we establish a new estimate for the degree of approximation of functions $f(x,y)$ f ( x , y ) belonging to the generalized Lipschitz class $Lip ((\xi _{1}, \xi _{2} );r )$ L i p ( ( ξ 1 , ξ 2 ) ; r ) , $r \geq 1$ r ≥ 1 , by double Hausdorff matrix summability means of double Fourier series. We also deduce the degree of approximation of functions from $Lip ((\alpha ,\beta );r )$ L i p ( ( α , β ) ; r ) and $Lip(\alpha ,\beta )$ L i p ( α , β ) in the form of corollary. We establish some auxiliary results on trigonometric approximation for almost Euler means and $(C, \gamma , \delta )$ ( C , γ , δ ) means.

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 Applications of Cesàro Submethod to Trigonometric Approximation of Signals (Functions) Belonging to ClassLip(α,p)inLp-Norm

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
M. L. Mittal ◽  
Mradul Veer Singh
Keyword(s):  
Trigonometric Approximation ◽  
Lipschitz Class ◽  
Approximation Of Functions ◽  
Approximation Of Signals

We prove two Theorems on approximation of functions belonging to Lipschitz classLip(α,p)inLp-norm using Cesàro submethod. Further we discuss few corollaries of our Theorems and compare them with the existing results. We also note that our results give sharper estimates than the estimates in some of the known results.

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