Resumen de Clarkson type inequalities and their relations to the concepts of type and cotype

Lars Erik Persson, Mikio Kato, Yasuji Takahashi

• We prove some multi-dimensional Clarkson type inequalities for Banach spaces.The exact relations between such inequalities and the concepts of type and cotypeare shown, which gives a conclusion in an extended setting to M. Milman’s ob-servation on Clarkson’s inequalities and type. A similar investigation concerningthe close connection between random Clarkson inequality and the correspondingconcepts of type and cotype is also included. The obtained results complement,unify and generalize several classical and some recent results of this type.