Characterization of the function spaces associated with weighted Sobolev spaces of the first order on the real line

2019 ◽  
Vol 74 (6) ◽  
pp. 1075-1115
Author(s):  
D. V. Prokhorov ◽  
V. D. Stepanov ◽  
E. P. Ushakova
Keyword(s):  
Sobolev Spaces ◽  
Real Line ◽  
Weighted Sobolev Spaces ◽  
Function Spaces ◽  
The Real ◽  
First Order

A duality principle in weighted Sobolev spaces on the real line

2015 ◽  
Vol 288 (8-9) ◽  
pp. 877-897 ◽  
Author(s):  
Simon P. Eveson ◽  
Vladimir D. Stepanov ◽  
Elena P. Ushakova
Keyword(s):  
Sobolev Spaces ◽  
Real Line ◽  
Weighted Sobolev Spaces ◽  
Duality Principle ◽  
The Real

Associated Spaces to Weighted Sobolev Spaces on the Real Line

2018 ◽  
Vol 481 (5) ◽  
pp. 486-489 ◽  
Author(s):  
D. Prokhorov ◽  
◽  
V. Stepanov ◽  
E. Ushakova ◽  
◽  
...  
Keyword(s):  
Sobolev Spaces ◽  
Real Line ◽  
Weighted Sobolev Spaces ◽  
The Real ◽  
Associated Spaces

Spaces Associated with Weighted Sobolev Spaces on the Real Line

2018 ◽  
Vol 98 (1) ◽  
pp. 373-376 ◽  
Author(s):  
D. V. Prokhorov ◽  
V. D. Stepanov ◽  
E. P. Ushakova
Keyword(s):  
Sobolev Spaces ◽  
Real Line ◽  
Weighted Sobolev Spaces ◽  
The Real

On weighted Sobolev spaces on the real line

2016 ◽  
Vol 93 (1) ◽  
pp. 78-81 ◽  
Author(s):  
D. V. Prokhorov ◽  
V. D. Stepanov ◽  
E. P. Ushakova
Keyword(s):  
Sobolev Spaces ◽  
Real Line ◽  
Weighted Sobolev Spaces ◽  
The Real

scholarly journals Higher Order Sobolev-Type Spaces on the Real Line

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Bogdan Bojarski ◽  
Juha Kinnunen ◽  
Thomas Zürcher
Keyword(s):  
Sobolev Spaces ◽  
Real Line ◽  
Finite Differences ◽  
Higher Order ◽  
Sobolev Type ◽  
The Real ◽  
Sobolev Functions ◽  
Sobolev Type Spaces ◽  
Type Spaces

This paper gives a characterization of Sobolev functions on the real line by means of pointwise inequalities involving finite differences. This is also shown to apply to more general Orlicz-Sobolev, Lorentz-Sobolev, and Lorentz-Karamata-Sobolev spaces.

scholarly journals A Remark on Isometries of Absolutely Continuous Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-3
Author(s):  
Alireza Ranjbar-Motlagh
Keyword(s):  
Continuous Function ◽  
Composition Operator ◽  
Real Line ◽  
Weighted Composition Operator ◽  
Function Spaces ◽  
Absolutely Continuous ◽  
The Real ◽  
Absolutely Continuous Function ◽  
Weighted Composition ◽  
Vector Valued

The purpose of this article is to study the isometries between vector-valued absolutely continuous function spaces, over compact subsets of the real line. Indeed, under certain conditions, it is shown that such isometries can be represented as a weighted composition operator.

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