Composition operators on Orlicz-Sobolev spaces
Ratan Kumar Giri, Debajyoti Choudhuri
TL;DR
This paper investigates the properties of composition operators on Orlicz-Sobolev spaces, providing conditions for their kernel, injectivity, and ascent characteristics, thereby advancing the understanding of their functional behavior.
Contribution
It introduces new criteria for the kernel and injectivity of composition operators and characterizes their ascent properties on Orlicz-Sobolev spaces.
Findings
Kernel of $C_T$ determined
Necessary and sufficient conditions for injectivity established
Characterization of operators with finite and infinite ascent
Abstract
The kernel of composition operator on Orlicz-Sobolev space is obtained. Using the kernel, a necessary and a sufficient condition for injectivity of composition operator has been established. Composition operators on Orlicz-Sobolev space with finite ascent as well as infinite ascent have been characterized.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Banach Space Theory · Advanced Harmonic Analysis Research