scholarly journals Corrigendum to “Variable Exponent Function Spaces related to a Sublinear Expectation”

2020 ◽  
Vol 2020 ◽  
pp. 1-1
Author(s):  
Bochi Xu
Keyword(s):  
Variable Exponent ◽  
Function Spaces ◽  
Sublinear Expectation

scholarly journals Variable Exponent Function Spaces related to a Sublinear Expectation

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Bochi Xu
Keyword(s):  
Stochastic Processes ◽  
Variable Exponent ◽  
Function Spaces ◽  
Sublinear Expectation ◽  
Kolmogorov’S Criterion

In this paper, variable exponent function spaces Lp·, Lbp·, and Lcp· are introduced in the framework of sublinear expectation, and some basic and important properties of these spaces are given. A version of Kolmogorov’s criterion on variable exponent function spaces is proved for continuous modification of stochastic processes.

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.

scholarly journals BMO Functions Generated by A X ℝ n Weights on Ball Banach Function Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Ruimin Wu ◽  
Songbai Wang
Keyword(s):  
Linear Operator ◽  
Function Space ◽  
Maximal Function ◽  
Lebesgue Space ◽  
Variable Exponent ◽  
Banach Function Space ◽  
Function Spaces ◽  
Banach Function Spaces ◽  
Bmo Functions ◽  
Littlewood Maximal Function

Let X be a ball Banach function space on ℝ n . We introduce the class of weights A X ℝ n . Assuming that the Hardy-Littlewood maximal function M is bounded on X and X ′ , we obtain that BMO ℝ n = α ln ω : α ≥ 0 , ω ∈ A X ℝ n . As a consequence, we have BMO ℝ n = α ln ω : α ≥ 0 , ω ∈ A L p · ℝ n ℝ n , where L p · ℝ n is the variable exponent Lebesgue space. As an application, if a linear operator T is bounded on the weighted ball Banach function space X ω for any ω ∈ A X ℝ n , then the commutator b , T is bounded on X with b ∈ BMO ℝ n .

scholarly journals Function Spaces with a Random Variable Exponent

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Boping Tian ◽  
Yongqiang Fu ◽  
Bochi Xu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Variable Exponent ◽  
Random Variable ◽  
Function Spaces ◽  
Partial Differential

The spaces with a random variable exponent and are introduced. After discussing the properties of the spaces and , we give an application of these spaces to the stochastic partial differential equations with random variable growth.

Embeddings in Grand Variable Exponent Function Spaces

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
David E. Edmunds ◽  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Variable Exponent ◽  
Function Spaces

scholarly journals Duality of Variable Exponent Triebel-Lizorkin and Besov Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Takahiro Noi
Keyword(s):  
Sobolev Spaces ◽  
Besov Spaces ◽  
Variable Exponent ◽  
Function Spaces ◽  
Bessel Potential ◽  
Lebesgue Spaces ◽  
Bessel Potential Spaces

We will prove the duality and reflexivity of variable exponent Triebel-Lizorkin and Besov spaces. It was shown by many authors that variable exponent Triebel-Lizorkin spaces coincide with variable exponent Bessel potential spaces, Sobolev spaces, and Lebesgue spaces when appropriate indices are chosen. In consequence of the results, these variable exponent function spaces are shown to be reflexive.

scholarly journals Singular integrals and potentials in some Banach function spaces with variable exponent

2003 ◽  
Vol 1 (1) ◽  
pp. 45-59 ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Stefan Samko
Keyword(s):  
Function Space ◽  
Singular Integral ◽  
Variable Exponent ◽  
Singular Integrals ◽  
Banach Function Space ◽  
Function Spaces ◽  
Power Weight ◽  
Banach Function Spaces ◽  
Dini Condition ◽  
Potential Type Operators

We introduce a new Banach function space - a Lorentz type space with variable exponent. In this space the boundedness of singular integral and potential type operators is established, including the weighted case. The variable exponentp(t)is assumed to satisfy the logarithmic Dini condition and the exponentβof the power weightω(t)=|t|βis related only to the valuep(0). The mapping properties of Cauchy singular integrals defined on Lyapunov curves and on curves of bounded rotation are also investigated within the framework of the introduced spaces.

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