scholarly journals Direct theorems of trigonometric approximation for variable exponent Lebesgue spaces

2019 ◽  
pp. 121-135
Author(s):  
Ramazan Akgün
Keyword(s):  
Variable Exponent ◽  
Trigonometric Approximation ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces

The refined direct and converse inequalities of trigonometric approximation in weighted variable exponent Lebesgue spaces

2011 ◽  
Vol 18 (3) ◽  
pp. 399-423
Author(s):  
Ramazan Akgün ◽  
Vakhtang Kokilashvili
Keyword(s):  
Variable Exponent ◽  
Trigonometric Approximation ◽  
Lebesgue Spaces ◽  
Converse Theorems ◽  
Variable Exponent Lebesgue Spaces ◽  
Weighted Variable

Abstract Refined direct and converse theorems of trigonometric approximation are proved in the variable exponent Lebesgue spaces with weights satisfying some Muckenhoupt Ap -condition. As a consequence, the refined versions of Marchaud and its converse inequalities are obtained.

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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