The Prague seminar on function spaces

## forthcoming program

March 21, 2018

Tomáš Roskovec (South Bohemian University, Èeské Budìjovice)

INTERPOLATION BETWEEN HÖLDER AND LEBESGUE SPACES WITH APPLICATIONS
(joint work with Filip Soudský and Anastasia Molchanova)

Abstract:

Classical interpolation inequality of the type $\|u\|_X ≤ C\|u\|_Y^{\theta} \|u\|_ Z^\theta$ is well known in the case when $X, Y, Z$ are Lebesgue spaces. In this paper we show that this result may be extended by replacing norms $\|\cdot\|_Y$ or $\|\cdot\|_X$ by suitable Hölder semi-norm. We shall even prove sharper version involving weak Lorentz norm. We apply this result to prove the Gagliardo-Nirenberg inequality for a wider scale of parameters.

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