Convexity and concavity constants in Lorentz and Marcinkiewicz spaces
We provide here the formulas for the q-convexity and q-concavity constants for function and sequence Lorentz spaces associated to either decreasing or increasing weights. It yields also the formula for the q-convexity constants in function and sequence Marcinkiewicz spaces. In this paper we extent and enhance the results from [G.J.O. Jameson, The q-concavity constants of Lorentz sequence spaces and related inequalities, Math. Z. 227 (1998) 129-142] and [A. Kamińska, A.M. Parrish, The q-concavity and q-convexity constants in Lorentz spaces, in: Banach Spaces and Their Applications in Analysis, Conference in Honor of Nigel Kalton, May 2006, Walter de Gruyter, Berlin, 2007, pp. 357-373].
Journal of Mathematical Analysis and Applications
Kamińska, A., & Parrish, A. (2008). Convexity and concavity constants in Lorentz and Marcinkiewicz spaces. Journal of Mathematical Analysis and Applications, 343 (1), 337-351. https://doi.org/10.1016/j.jmaa.2008.01.034