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Inclusions Among Mixed-Norm Lebesgue Spaces, Wayne R. Grey
Inclusions Among Mixed-Norm Lebesgue Spaces, Wayne R. Grey
Electronic Thesis and Dissertation Repository
A mixed LP norm of a function on a product space is the
result of successive classical Lp 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 Lp spaces.
The two-variable problem (with four Lp exponents, two for
each mixed norm) is studied extensively. The problem's ``unpermuted"
case simply reduces to a question of Lp embeddings. The other,
``permuted" case further divides, depending on the values of the
Lp exponents. Often, …