scholarly journals Uniform boundedness of Kantorovich operators in variable exponent Lebesgue spaces

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5755-5765 ◽  
Author(s):  
Rabil Ayazoglu ◽  
Sezgin Akbulut ◽  
Ebubekir Akkoyunlu
Keyword(s):  
Variable Exponent ◽  
Closed Interval ◽  
Uniform Boundedness ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces ◽  
The Difference ◽  
Upper Estimate ◽  
Kantorovich Operators ◽  
Uniformly Bounded

In this paper, the Kantorovich operators Kn, n ? N are shown to be uniformly bounded in variable exponent Lebesgue spaces on the closed interval [0; 1]. Also an upper estimate is obtained for the difference Kn(f)-f for functions f of regularity of order 1 and 2 measured in variable exponent Lebesgue spaces, which is of interest on its own and can be applied to other problems related to the Kantorovich operators.

An Almost Greedy Uniformly Bounded Orthonormal Basis in 𝐿𝑝(·)([0, 1]) Spaces

2009 ◽  
Vol 16 (3) ◽  
pp. 465-474
Author(s):  
Ana Danelia ◽  
Ekaterine Kapanadze
Keyword(s):  
Maximal Operator ◽  
Variable Exponent ◽  
Orthonormal Basis ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces ◽  
Greedy Basis ◽  
Littlewood Maximal Operator ◽  
Uniformly Bounded

Abstract We construct a uniformly bounded orthonormal almost greedy basis for the variable exponent Lebesgue spaces 𝐿𝑝(·)([0, 1]), 1 < 𝑝– ≤ 𝑝+ ≤ 2 (or 2 ≤ 𝑝– ≤ 𝑝+ < ∞), when the diadic Hardy–Littlewood maximal operator is bounded on these spaces.

scholarly journals Uniform boundedness of Szász-Mirakjan-Kantorovich operators in Morrey spaces with variable exponents

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2109-2121
Author(s):  
Yoshihiro Sawano ◽  
Xinxin Tian ◽  
Jingshi Xu
Keyword(s):  
Maximal Operator ◽  
Uniform Boundedness ◽  
Morrey Spaces ◽  
Variable Exponents ◽  
Lebesgue Spaces ◽  
Littlewood Maximal Operator ◽  
Kantorovich Operators ◽  
Uniformly Bounded

The Sz?sz-Mirakjan-Kantorovich operators and the Baskakov-Kantorovich operators are shown to be controlled by the Hardy-Littlewood maximal operator. The Sz?sz-Mirakjan-Kantorovich operators and the Baskakov-Kantorovich operators turn out to be uniformly bounded in Lebesgue spaces and Morrey spaces with variable exponents when the integral exponent is global log-H?lder continuous.

scholarly journals Estimates of Fractional Integral Operators on Variable Exponent Lebesgue Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Canqin Tang ◽  
Qing Wu ◽  
Jingshi Xu
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Weak Type ◽  
Type Inequality ◽  
Integral Operators ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Variable Exponent Lebesgue Spaces

By some estimates for the variable fractional maximal operator, the authors prove that the fractional integral operator is bounded and satisfies the weak-type inequality on variable exponent Lebesgue spaces.

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