Some Properties of Banach Space-Valued Lp
Spaces
Daehan Park

Lp spaces are one of the most popular function spaces for mathematicians whatever his major is. Also the Banach Space is well-known space with many good properties. Most of people know the properties of Lp spaces in the case of real or complex valued. In study of many cases, however, people encounter a function valued(or a Banach space valued) Lp space, and desire these spaces to have same propery as real or complex valued ones. The examples of such spaces are Hp, Lp(Hp). In this talk the speaker will say about some properties of Lp spaces, consist of functions whose values are in a Banach space. From the simplest properties like Holder inequality and completeness, the talk goes to the duality of a Banach space valued Lp spaces with additional conditions. The given facts are frequently used in the study of SPDE, PDE and any area in which the function space valued Lp spaces are needed. The audience just needs a short knowledge on real or complex valued Lp space and Banach spaces.