Analytic variable exponent Hardy spaces. (English) Zbl 1461.30122

Chacón, Gerardo A.; Chacón, Gerardo R.

Adv. Oper. Theory 4, No. 4, 738-749 (2019).

Summary: 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-Hölder condition, and \(H^{p(\cdot)}\neq H^q\) for every constant exponent \(q\in(1,\infty)\). We also consider the variable exponent version of the Hardy space on the upper-half plane.

MSC:

30H10	Hardy spaces
31A05	Harmonic, subharmonic, superharmonic functions in two dimensions

Keywords:

variable exponent analytic Hardy space; variable exponent harmonic Hardy space