On Orlicz classes defined in terms of associated weight functions

Area of Science:

• Real Analysis
• Functional Analysis
• Theory of Function Spaces

Background:

• N-functions are fundamental to Orlicz classes and spaces.
• Associated weight functions are key in ultradifferentiable function classes.
• Weight sequences provide underlying structure for weight functions.

Purpose of the Study:

• To characterize N-function properties using weight sequences.
• To investigate the applicability of this framework to abstract N-functions.
• To establish a link between complementary N-functions and dual sequences.

Main Methods:

• Analysis of N-functions via associated weight functions.
• Characterization of N-function properties using weight sequences.
• Exploration of abstract N-function frameworks.

Main Results:

• Several known N-function properties are expressed purely in terms of weight sequences.
• This allows for the construction of N-function examples and counter-examples.
• A connection is established between the complementary N-function and dual sequences.

Conclusions:

• The weight sequence framework offers a simplified and powerful tool for studying N-functions.
• This approach enhances understanding of Orlicz spaces and ultradifferentiable functions.
• The established connection provides new insights into dual sequences and complementary N-functions.