Rupert L. Frank

activity

20162026

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math.AP2026

Sharp Sobolev inequalities under first moment constraints

Rupert L. Frank, Tianling Jin, Hua-Yang Wang +1

Let $n \geq 2$ and $1 < p < n$ . We study sharp Sobolev inequalities on the round sphere $S^{n}$ for functions $u \in W^{1, p} (S^{n})$ satisfying $\int_{\mathbb{S}^n}x|u|^{np/…

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…

Sharp Sobolev inequalities under first moment constraints

Another characterization of W˙1,p(Rd)

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