Multilinear singular integrals and commutators in variable exponent Lebesgue spaces

2010 ◽  
Vol 25 (1) ◽  
pp. 69-77 ◽  
Author(s):  
Ai-wu Huang ◽  
Jing-shi Xu
Keyword(s):  
Variable Exponent ◽  
Singular Integrals ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces ◽  
Multilinear Singular Integrals

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.

scholarly journals Multilinear Singular Integrals and Commutators on Herz Space with Variable Exponent

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Amjad Hussain ◽  
Guilian Gao
Keyword(s):  
Singular Integral ◽  
Variable Exponent ◽  
Singular Integrals ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Herz Space ◽  
Herz Spaces ◽  
Multilinear Singular Integrals

The paper establishes some sufficient conditions for the boundedness of singular integral operators and their commutators from products of variable exponent Herz spaces to variable exponent Herz 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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