A multilinear Rellich inequality

Abstract

. We prove a multilinear variant of the Rellich inequality on the real line. In particular, we establish the weighted inequality with a positive function w on ( 0 , b − a )) , where − ∞ (cid:2) a < b (cid:2) + ∞ , m is a positive integer, δ ( x ) = min { x − a , b − x } is the distance function on ( a , b ) , and 1 / p = ∑ mj = 1 1 / p j , p j > 1, j = 1 ,..., m . As a corollary we derive the following estimate b Mathematics subject classi fi cation (2010): 26A42, 35A22, 35A23.