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Zeitschrift für Analysis und ihre Anwendungen

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Volume 38, Issue 4, 2019, pp. 419–437
DOI: 10.4171/ZAA/1644

Published online: 2019-10-23

New Young Inequalities and Applications

Pedro Fernández-Martínez[1] and Eduardo Brandani da Silva[2]

(1) Universidad de Murcia, Spain
(2) Universidade Estadual de Maringá, Paraná, Brazil

We establish upper bounds for the convolution operator acting between interpolation spaces. This gives new Young inequalities in the context of Lorentz–Karamata spaces, grand Lebesgue spaces and small Lebesgue spaces besides many other known results. Furthermore, we use this abstract Young inequality to prove a bilinear interpolation theorem for limit interpolation methods. Finally, we show applications to the study of bilinear multipliers.

Keywords: Convolution operator, interpolation theory, function spaces, bilinear multipliers

Fernández-Martínez Pedro, Brandani da Silva Eduardo: New Young Inequalities and Applications. Z. Anal. Anwend. 38 (2019), 419-437. doi: 10.4171/ZAA/1644