Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Lipschitz spaces on stratified groups
HTML articles powered by AMS MathViewer

by Steven G. Krantz PDF
Trans. Amer. Math. Soc. 269 (1982), 39-66 Request permission

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 $||f(g\exp {X_i} \cdot )|| \in {\Lambda _\alpha }({\mathbf {R}})$, 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.
References
Similar Articles
Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 269 (1982), 39-66
  • MSC: Primary 22E30; Secondary 22E25, 35H05, 46E35, 58G05
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0637028-6
  • MathSciNet review: 637028