Generalized potentials in variable exponent Lebesgue spaces on homogeneous spaces

2011 ◽  
Vol 284 (1) ◽  
pp. 53-66 ◽  
Author(s):  
Mubariz G. Hajibayov ◽  
Stefan Samko
Keyword(s):  
Variable Exponent ◽  
Homogeneous Spaces ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces

Maximal and Calderón–Zygmund operators in grand variable exponent Lebesgue spaces

2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Variable Exponent ◽  
Function Spaces ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces

AbstractNew function spaces

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.

The Riemann boundary value problem in the class of Cauchy type integrals with densities of grand variable exponent Lebesgue spaces

2016 ◽  
Vol 23 (4) ◽  
pp. 551-558 ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi ◽  
Vakhtang Paatashvili
Keyword(s):  
Boundary Value Problem ◽  
Variable Exponent ◽  
Boundary Value ◽  
Function Spaces ◽  
Cauchy Type ◽  
Riemann Boundary Value Problem ◽  
Lebesgue Spaces ◽  
Standard Type ◽  
Riemann Boundary ◽  
Variable Exponent Lebesgue Spaces

AbstractThe present paper deals with the Riemann boundary value problem for analytic functions in the framework of the new function spaces introduced by the first two authors, the so-called grand variable exponent Lebesgue spaces which unify two non-standard type function spaces: variable exponent Lebesgue spaces and grand Lebesgue spaces.

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