For $p > 2$ Hausdorff-Young does not hold for the Laplace Transform on $L^p(0,\infty)$ (Open)

Summary: A simple example is given of a function in $L^p(0,\infty)$ whose Laplace transform does not belong to the dual space.

Classification: Primary, Classical Analysis; Secondary, Integrals

Anatoli Merzon
Universidad Michoacana de San Nicolas de Hidalgo
Morelia, Michoacan, Mexico
Email: anatoli@ifm.umich.mx
Phone: +52 443-340-45-30
Fax: +52 443-322-35-99 ext 4133

Sergey Sadov
Department of Mathematics and Statistics
Memorial University of Newfoundland
St. John's, Canada
Email: sergey@mun.ca (address for correspondence)
Phone: 709-864-4358
Fax: 709-864-3010

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