scholarly journals On *-Boundedness and *-Local Boundedness of Non-Newtonian Superposition Operators in $c_{0,\alpha }~$and $c_{\alpha }$ to $\ell _{1,\beta }$

2021 ◽  
Author(s):  
Fatmanur ERDOGAN ◽  
Birsen SAĞIR DUYAR
Keyword(s):  
Local Boundedness ◽  
Superposition Operators

LOCAL BOUNDEDNESS OF NONAUTONOMOUS SUPERPOSITION OPERATORS IN

2015 ◽  
Vol 92 (2) ◽  
pp. 325-341 ◽  
Author(s):  
PIOTR KASPRZAK ◽  
PIOTR MAĆKOWIAK
Keyword(s):  
Bounded Variation ◽  
Bounded Function ◽  
Functions Of Bounded Variation ◽  
Superposition Operator ◽  
Local Boundedness ◽  
Superposition Operators ◽  
Locally Bounded Function

The main goal of this paper is to give the answer to one of the main problems of the theory of nonautonomous superposition operators acting in the space of functions of bounded variation in the sense of Jordan. Namely, we prove that if the superposition operator maps the space $BV[0,1]$ into itself, then it is automatically locally bounded, provided its generator is a locally bounded function.

Uniform continuity of nonautonomous superposition operators in ΛBV-spaces

2019 ◽  
Vol 31 (3) ◽  
pp. 713-726
Author(s):  
Jacek Gulgowski
Keyword(s):  
Sufficient Conditions ◽  
Uniform Continuity ◽  
Regular Functions ◽  
Superposition Operators

Abstract In this paper we investigate the problem of uniform continuity of nonautonomous superposition operators acting between spaces of functions of bounded Λ-variation. In particular, we give the sufficient conditions for nonautonomous superposition operators to continuously map a space of functions of bounded Λ-variation into itself. The conditions cover the generators being functions of {C^{1}} -class (in view of two variables), but also allow for less regular functions, including discontinuous generators.

scholarly journals On Generalized Step-Functions and Superposition Operators

2004 ◽  
Vol 11 (4) ◽  
pp. 753-758
Author(s):  
A. Kharazishvili
Keyword(s):  
Step Functions ◽  
Functions Of Two Variables ◽  
Superposition Operators

Abstract For a given σ-ideal of sets, the notion of a generalized stepfunction is introduced and investigated in connection with the problem of sup-measurability of certain functions of two variables, regarded as superposition operators.

Local boundedness of minimizers in a limit case

1990 ◽  
Vol 69 (1) ◽  
pp. 19-25 ◽  
Author(s):  
Nicola Fusco ◽  
Carlo Sbordone
Keyword(s):  
Limit Case ◽  
Local Boundedness
Sign in / Sign up

Export Citation Format

Share Document