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Abstract
If f is a function of class Lp
on the torus and if the subset E of
is the peak set of a function of class Ap
(UN
), then there is a function g in A
p − l, α
(UN
for all α between zero and one with g = f on E. The peak sets of functions of class Ap
(Un
) lie in locally closed interpolation submanifolds of the torus of class Lp
. but an example shows that they need not lie in closed interpolation submanifolds.
1Research supported in part by National Science Foundation Grants MCS810768 and MCS 8301142.
1Research supported in part by National Science Foundation Grants MCS810768 and MCS 8301142.
Notes
1Research supported in part by National Science Foundation Grants MCS810768 and MCS 8301142.