# Journal of Operator Theory

Volume 66, Issue 1, Summer 2011 pp. 125-144.

Hyperinvariant subspaces for weighted composition operators on $L^p([0,1]^d)$**Authors**: George Androulakis (1) and Antoine Flattot (2)

**Author institution:**(1) Department of Mathematics, University of South Carolina, Columbia, SC 29208, U.S.A.

(2) Department of Mathematics, University of South Carolina, Columbia, SC 29208, U.S.A.

**Summary:**The main result of this paper is the existence of a hyperinvariant subspace of the weighted composition operator $Tf=vf\circ\tau$ on $L^p([0,1]^d)$, ($1 \leqslant p \leqslant \infty$) when the weight $v$ is in the class of "generalized polynomials" and the composition map is a bijective ergodic transform satisfying a given discrepancy estimates. The work is based on the construction of a functional calculus initiated by Wermer and generalized by Davie.

**Keywords:**invariant subspace, weighted composition operator, discrepancy, functional calculus

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