On some interpolation inequalities between Hölder and Lebesgue's spaces

2024/09/21 by S. P. Degtyarev, Degtyarev, Sergey P.
Mathematics · #Advanced Harmonic Analysis Research #Mathematical functions and polynomials #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.2409.14102

Abstract

We present a simple proof of some interpolation inequalities between Hölder and Lebesgue's spaces. As an example, to demonstrate the simplicity of their applications to nonlinear PDE, we give also a simple proof of an a-priory estimate in a smooth Hölder class for a solution to some quasilinear parabolic initial boundary value problem.

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