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- W2023362277 abstract "Let $G$ be a connected, simply connected nilpotent Lie group. Call $G$ stratified if its Lie algebra $mathfrak {g}$ has a direct sum decomposition $mathfrak {g} = {V_1} oplus cdots oplus {V_m}$ with $[{V_i},{V_j}] = {V_{i + j}}$ for $i + j leqslant m$, $[{V_{i,}}{V_j}] = 0$ for $i + j > m$. Let ${ {X_1}, ldots ,{X_n}}$ be a vector space basis for ${V_1}$. Let $f in C(G)$ satisfy $||f(gexp {X_i} cdot )|| in {Lambda _alpha }({mathbf {R}})$, uniformly in $g in G$, where ${Lambda _alpha }$ is the usual Lipschitz space and $0 < alpha < infty$. It is proved that, under these circumstances, it holds that $f in {Gamma _alpha }(G)$ where ${Gamma _alpha }$ is the nonisotropic Lipschitz space of Folland. Applications of this result to interpolation theory, hypoelliptic partial differential equations, and function theory are provided." @default.
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- W2023362277 date "1982-01-01" @default.
- W2023362277 modified "2023-10-04" @default.
- W2023362277 title "Lipschitz spaces on stratified groups" @default.
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- W2023362277 doi "https://doi.org/10.1090/s0002-9947-1982-0637028-6" @default.
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