391 citations · 1.8k across the 147 of their papers we have counts for
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A characterization of
Rupert L. Frank
For we give a characterization of the Sobolev space in terms of the oscillations of a function on balls of varying centers and radii. Our w…
Lieb-Thirring inequalities and other functional inequalities for orthonormal systems
Rupert L. Frank
We review recent results on functional inequalities for systems of orthonormal functions. The key finding is that for various operators the orthonormality leads to a gain over a si…
Inequalities that sharpen the triangle inequality for sums of functions in
Eric A. Carlen, Rupert L. Frank, Elliott H. Lieb
We study inequalities that sharpen the triangle inequality for sums of functions in .
Inequalities for -norms that sharpen the triangle inequality and complement Hanner's Inequality
Eric A. Carlen, Rupert L. Frank, Paata Ivanisvili +1
In 2006 Carbery raised a question about an improvement on the naïve norm inequality for two functions in of any measure spac…
Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems
Jacopo Bellazzini, Rupert L. Frank, Nicola Visciglia
In this paper we study the existence of maximizers for two families of interpolation inequalities, namely a generalized Gagliardo-Nirenberg inequality and a new inequality involvin…
Fractional Hardy-Sobolev-Maz'ya inequality for domains
Bartłomiej Dyda, Rupert L. Frank
We prove a fractional version of the Hardy--Sobolev--Maz'ya inequality for arbitrary domains and norms with . This inequality combines the fractional Sobolev and the…