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Optimal Weak Parallelogram Constants For L-P Spaces, Raymond Cheng, Javad Mashreghi, William T. Ross
Optimal Weak Parallelogram Constants For L-P Spaces, Raymond Cheng, Javad Mashreghi, William T. Ross
Department of Math & Statistics Faculty Publications
Inspired by Clarkson's inequalities for L-p and continuing work from [5], this paper computes the optimal constant C in the weak parallelogram laws parallel to f + g parallel to(r )+ C parallel to f - g parallel to(r )= 2(r-1 )(parallel to f parallel to(r) + parallel to g parallel to(r)) for the L-p spaces, 1 < p < infinity.