Malliavin Derivatives in Spaces with Variable Exponents

Abstract

Spaces with variable exponents Lpx(H,μ) and Lpx(H,μ;H) are introduced. After discussing some approximation results of Lpx(H,μ), Sobolev spaces on H with variable exponents are introduced. At last, we define Malliavin derivatives in Lpx(H,μ) and discuss some properties of Malliavin derivatives in Lpx(H,μ).