engleski

Boundedness of pseudodifferential operators on mixed-norm spaces

Pseudodifferential operators have nice boundedness properties on Sobolev spaces. These properties are consequences of L^p boundedness of zeroth order operators, a classical result improving Hormander-Mihlin theorem. We prove the extension of the above result to mixed-norm L^p spaces (introduced by Benedek & Panzone in 1961), by applying the Calderon-Zygmund decomposition and generalised Marcinkiewicz interpolation theorem. Finally, we show some extensions to boundedness of classical pseudodifferential operators (of any order) on Sobolev spaces, having possible application to the theory of partial differential equations.

pseudodifferential operator ; mixed-norm Lebesgue space

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