Type and cotype are computed for Banach spaces generated by some positive sublinear operators and Banach function spaces. Applications of the results yield that under certain assumptions Clarkson's inequalities hold in these spaces.
Qiu, J. H., & McKennon, K. (1991). BANACH-MACKEY SPACES. International Journal of Mathematics and Mathematical Sciences, 1991(), 215-219. https://doi.org/10.1155/S0161171291000224
Soybas, D. (2012). The (D) Property in Banach Spaces. Abstract and Applied Analysis, 2012(), 11-17-601. https://doi.org/10.1155/2012/754531
Kaushik, S. K. (2007). Some Results Concerning Frames in Banach Spaces. Tamkang Journal of Mathematics, 38(3), 267-276. https://www.airitilibrary.com/Article/Detail?DocID=00492930-200709-38-3-267-276-a