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Inclusions Among Mixed-Norm Lebesgue Spaces, Wayne R. Grey

Electronic Thesis and Dissertation Repository

A mixed L^P norm of a function on a product space is the

result of successive classical L^p norms in each variable,

potentially with a different exponent for each. Conditions to

determine when one mixed norm space is contained in another are

produced, generalizing the known conditions for embeddings

of L^p spaces.

The two-variable problem (with four L^p exponents, two for

each mixed norm) is studied extensively. The problem's ``unpermuted"

case simply reduces to a question of L^p embeddings. The other,

``permuted" case further divides, depending on the values of the

L^p exponents. Often, …