Page 1 Next

Displaying 1 – 20 of 1382

Showing per page

A characterization of linear automorphisms of the Euclidean ball

Hidetaka Hamada, Tatsuhiro Honda (1999)

Annales Polonici Mathematici

Let B be the open unit ball for a norm on n . Let f:B → B be a holomorphic map with f(0) = 0. We consider a condition implying that f is linear on n . Moreover, in the case of the Euclidean ball , we show that f is a linear automorphism of under this condition.

A counter-example in singular integral theory

Lawrence B. Difiore, Victor L. Shapiro (2012)

Studia Mathematica

An improvement of a lemma of Calderón and Zygmund involving singular spherical harmonic kernels is obtained and a counter-example is given to show that this result is best possible. In a particular case when the singularity is O(|log r|), let f C ¹ ( N 0 ) and suppose f vanishes outside of a compact subset of N , N ≥ 2. Also, let k(x) be a Calderón-Zygmund kernel of spherical harmonic type. Suppose f(x) = O(|log r|) as r → 0 in the L p -sense. Set F ( x ) = N k ( x - y ) f ( y ) d y x N 0 . Then F(x) = O(log²r) as r → 0 in the L p -sense, 1 < p < ∞....

Currently displaying 1 – 20 of 1382

Page 1 Next