Malliavin Derivatives in Spaces with Variable Exponents

Abstract EN

Spaces with variable exponents L p x ( H , μ ) and L p x ( H , μ ; H ) areintroduced.

After discussing some approximation results of L p x ( H , μ ) , Sobolev spaces on H with variable exponents are introduced.

At last, we define Malliavin derivatives in L p x ( H , μ ) and discuss some properties of Malliavin derivatives in L p x ( H , μ ) .