In Richard v. Hoechst Celanese Chem. Group, Inc., 355 F.3d 345, 350 (5th Cir. 2003), the Fifth Circuit held that:

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Under the Rooker/Feldman doctrine, "lower federal courts lack [subject-matter] jurisdiction to review state court judgments when the constitutional claims are 'inextricably intertwined' with [a] challenged state court judgment."

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Id. (citing Feldman, 460 U.S. at 483 n.16).

This Fifth Circuit decision also sets forth three separate tests for what actions by a private actor constitutes state action:

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According to the public function test, a private entity acts under color of state law when the entity performs a function which is "exclusively reserved to the state." Flagg Bros., 436 U.S. at 157-58. (internal quotations omitted); Wong v. Stripling, 881 F.2d 200, 202 (5th Cir. 1989). The state compulsion (or coercion) test holds the state responsible "for a private decision only when [the state] has exercised coercive power or has provided such significant encouragement, either overt or covert, that the choice must in law be deemed to be that of the State." Blum v. Yaretsky, 457 U.S. 991, 1004, 73 L. Ed. 2d 534, 102 S. Ct. 2777 (1982) (internal quotations omitted). Similarly, the nexus or state action test finds state action where the state has "so far insinuated itself into a position of interdependence with the [private actor] that it was a joint participant in the enterprise." Jackson v. Metropolitan Edison Co., 419 U.S. 345, 357-58, 42 L. Ed. 2d 477, 95 S. Ct. 449 (1974); see also Lugar, 457 U.S. at 941-42 (1982).

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Richard v. Hoechst Celanese Chem. Grp., Inc., 355 F.3d 345, 352 (5th Cir. 2003)