 Sum of Lp spaces

ID: sum-of-lp-spaces

f = g + h

with

g \in L^{p_{0}}

and

h \in L^{p_{1}}

, with norm

in f_{f = g + h} (∥ g ∥_{p_{0}} + ∥ h ∥_{p_{1}})

. It is a Banach space. One construction identifies it with the quotient of

L^{p_{0}} \oplus_{1} L^{p_{1}}

by the closed kernel of the addition map. Bounded endpoint operators are therefore bounded on the corresponding sum spaces.

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