To precisely state the inequality, let L 2 ( R n ) denote the usual Hilbert space of square-integrable functions, and H 1 ( R n ) the Sobolev space of square-integrable functions with square-integrable derivatives. Let f , A 1 , … … , A n be measurable functions on R n and suppose that A j ∈ ∈ L loc 2 ( R n ) is real-valued, f is complex-valued, and f , ( ∂ ∂ 1 + i A 1 ) f , … … , ( ∂ ∂ n + i A n ) f ∈ ∈ L 2 ( R n ) . Then for almost every x ∈ ∈ R n , | ∇ ∇ | f | ( x ) | ≤ ≤ | ( ∇ ∇ + i A ) f ( x ) | . In particular, | f | ∈ ∈ H 1 ( R n ) .