Analytic variable exponent Hardy spaces

Document Type: Original Article

Authors

1 ‎Universidad Antonio Narino‎, ‎Colombia

2 ‎Gallaudet University, USA

Abstract

We introduce a variable exponent version of the Hardy space of analytic functions on the unit disk, we show some properties of the space, and give an example of a variable exponent $p(\cdot)$ that satisfies the $log$-H\"older condition, and $H^{p(\cdot)}neq H^q$ for every constant exponent $1<q<\infty$. We also consider the variable exponent version of the Hardy space on the upper-half plane.

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