Frederick Gehring

Frederick William Gehring

Personal life

Both of Fred Gehring's parents graduated from the

Gehring served as a Benjamin Peirce instructor at Harvard University for three years after completing his doctoral work at the University of Cambridge. In 1955 he returned to Ann Arbor, MI, to assume a post on the faculty of the Department of Mathematics at the University of Michigan where he worked until he retired at age 70. During this time he supervised 29 Ph.D. students, six of whom are women, as well as 40 postdoctoral visitors.^[3] He also served as chairman of the department on three separate occasions, serving for a total of eight years.

Honors and awards

• 1986 – awarded the Order of the White Rose of Finland, Commander class, Finland's highest scientific honor for foreigners.
• 1989 – elected to the National Academy of Sciences.
• 1995 – awarded the Onsager Medal.
• 1997 – received an honorary degree (dr. philos. h.c.) from The Norwegian University of Science and Technology (NTNU).^[4]
• 2006 – awarded the
  Steele Prize
  for Lifetime Achievement.

Gehring's Lemma

In a 1973 paper^[5] which has been cited over 800 times, Gehring proved the following lemma:^[6]
Assume that ${\displaystyle f}$ is a non–negative locally integrable function on Rⁿ and 1 < ${\displaystyle p}$ < ∞. If there is a constant c₁ such that the inequality

${\displaystyle {\begin{aligned}&\left(\int _{B}|f(x)|^{p}\,dx\right)^{\frac {1}{p}}\end{aligned}}}$ ≤ c₁${\displaystyle {\begin{aligned}&\left(\int _{B}f(x)\,dx\right)\end{aligned}}}$

holds for all balls B of Rⁿ, then there exists ${\displaystyle \varepsilon }$ > 0 and there exists a constant c₂ such that

${\displaystyle {\begin{aligned}&\left(\int _{B}|f(x)|^{p+\varepsilon }\,dx\right)^{\frac {1}{p+\varepsilon }}\end{aligned}}}$ ≤ c₂${\displaystyle {\begin{aligned}&\left(\int _{B}f(x)\,dx\right)\end{aligned}}}$ holds for all balls B of Rⁿ.

Selected publications

• Frederick W. Gehring,
  ISBN 978-0-8218-4360-4.{{cite book}}: CS1 maint: multiple names: authors list (link)^[7]
• Martin, Gaven (2017), "Frederick W. Gehring : A Biographical Memoir" (PDF), National Academy of Sciences, Bibliographical Memoirs, pp. 1–19

References