*
*
*The
Prague seminar on function spaces*

##
forthcoming program

**March 21, 2018**

**Tomáš Roskovec (**South Bohemian University, České Budėjovice**)**

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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