scholarly journals Intrinsic Characterization and the Extension Operator in Variable Exponent Function Spaces on Special Lipschitz Domains

2017 ◽  
pp. 175-192 ◽  
Author(s):  
Henning Kempka
Keyword(s):  
Variable Exponent ◽  
Extension Operator ◽  
Function Spaces ◽  
Lipschitz Domains ◽  
Intrinsic Characterization

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

Trace/extension operators in rough domains and applications to partial differential equations

2015 ◽  
Author(s):  
◽  
Kevin Brewster
Keyword(s):  
Dirichlet Boundary ◽  
Boundary Value ◽  
Weighted Sobolev Spaces ◽  
Extension Operator ◽  
Extension Theory ◽  
Lipschitz Domains ◽  
Poisson Boundary ◽  
Ellipticity Condition ◽  
University Of Missouri ◽  
The University

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Trace and extension theory lay the foundation for solving a plethora of boundary value problems. In developing this theory, one typically needs well-behaved extension operators from a specified domain to the entire Euclidean space. Historically, three extension operators have developed much of the theory in the setting of Lipschitz domains (and rougher domains); those due to A.P. Calderon, E.M. Stein, and P.W. Jones. In this dissertation, we generalize Stein's extension operator to weighted Sobolev spaces and Jones' extension operator to domains with partially vanishing traces. We then develop a rich trace/extension theory as a tool in solving a Poisson boundary value problem with Dirichlet boundary condition where the differential operator in question is of second order in divergence form with bounded coefficients satisfying the Legendre-Hadamard ellipticity condition.

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.

scholarly journals On Burenkov's extension operator preserving Sobolev-Morrey spaces on Lipschitz domains

2016 ◽  
Vol 290 (1) ◽  
pp. 37-49 ◽  
Author(s):  
Maria Stella Fanciullo ◽  
Pier Domenico Lamberti
Keyword(s):  
Extension Operator ◽  
Morrey Spaces ◽  
Lipschitz Domains

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.

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