Variable Exponent Fock Spaces

TL;DR

This paper introduces Variable Exponent Fock Spaces, exploring their fundamental properties like evaluation functional boundedness, polynomial density, Bergman projection boundedness, and duality, expanding the understanding of these generalized function spaces.

Contribution

The paper presents the first systematic study of Variable Exponent Fock Spaces, establishing key properties and foundational results for this new class of function spaces.

Findings

Evaluation functionals are bounded in Variable Exponent Fock Spaces.

Polynomials are dense in these spaces.

A Bergman-type projection is bounded in this setting.

Abstract

In this article we introduce Variable exponent Fock spaces and study some of their basic properties such as the boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality.