Rupert L. Frank

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20162026

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math.FA2026

Another characterization of $W ˙^{1, p} (R^{d})$

Rupert L. Frank

We improve an earlier characterization of the Sobolev space $W ˙^{1, p} (R^{d})$ , $1 < p < \infty$ , in terms of the oscillations of a function on balls of varying centers and ra…

math.FA2024

Endpoint Schatten class properties of commutators

Rupert L. Frank, Fedor Sukochev, Dmitriy Zanin

We study trace ideal properties of the commutators $[(- Δ)^{\frac{ε}{2}}, M_{f}]$ of a power of the Laplacian with the multiplication operator by a function $f$ on $R^{d}$ . For a c…

Another characterization of W˙1,p(Rd)

Endpoint Schatten class properties of commutators

Another characterization of $W ˙^{1, p} (R^{d})$