Boundedness in Lebesgue Spaces with Variable Exponent of the Cauchy Singular Operator on Carleson Curves

2007 ◽  
pp. 167-186 ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Vakhtang Paatashvili ◽  
Stefan Samko
Keyword(s):  
Variable Exponent ◽  
Singular Operator ◽  
Lebesgue Spaces ◽  
Cauchy Singular Operator

Approximation by trigonometric polynomials in the framework of variable exponent grand Lebesgue spaces

2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Nina Danelia ◽  
Vakhtang Kokilashvili
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Trigonometric Polynomials ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Space ◽  
Grand Lebesgue Spaces ◽  
Direct And Inverse Theorems ◽  
Inverse Theorems ◽  
Grand Lebesgue Space

AbstractIn this paper we establish direct and inverse theorems on approximation by trigonometric polynomials for the functions of the closure of the variable exponent Lebesgue space in the variable exponent grand Lebesgue space.

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 A trace inequality for generalized potentials in Lebesgue spaces with variable exponent

2004 ◽  
Vol 2 (1) ◽  
pp. 55-69 ◽  
Author(s):  
David E. Edmunds ◽  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Variable Exponent ◽  
Homogeneous Type ◽  
Trace Inequality ◽  
Spaces Of Homogeneous Type ◽  
Weighted Inequality ◽  
Euclidean Spaces ◽  
Riesz Potentials ◽  
Lebesgue Spaces ◽  
Fractal Sets

A trace inequality for the generalized Riesz potentialsIα(x)is established in spacesLp(x)defined on spaces of homogeneous type. The results are new even in the case of Euclidean spaces. As a corollary a criterion for a two-weighted inequality in classical Lebesgue spaces for potentialsIα(x)defined on fractal sets is derived.

scholarly journals Variable Exponent Spaces of Analytic Functions

2020 ◽  
Author(s):  
Gerardo A. Chacón ◽  
Gerardo R. Chacón
Keyword(s):  
Hardy Spaces ◽  
Measurable Function ◽  
Analytic Functions ◽  
Variable Exponent ◽  
Bergman Spaces ◽  
Lebesgue Spaces ◽  
Basic Properties ◽  
Variable Exponent Spaces ◽  
Real Functions ◽  
Spaces Of Analytic Functions

Variable exponent spaces are a generalization of Lebesgue spaces in which the exponent is a measurable function. Most of the research done in this topic has been situated under the context of real functions. In this work, we present two examples of variable exponent spaces of analytic functions: variable exponent Hardy spaces and variable exponent Bergman spaces. We will introduce the spaces together with some basic properties and the main techniques used in the context. We will show that in both cases, the boundedness of the evaluation functionals plays a key role in the theory. We also present a section of possible directions of research in this topic.

On the boundedness of Cauchy singular operator from the spaceL p toL q ,p>q>-1

1994 ◽  
Vol 1 (4) ◽  
pp. 395-403
Author(s):  
G. Khuskivadze ◽  
V. Paatashvili
Keyword(s):  
Singular Operator ◽  
Cauchy Singular Operator
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