-closed extension of CR-forms with singularities on a generic manifold.
The main purpose of this note is to give a new characterization of the well-known Carleson measure in terms of the integral for functions with their derivatives on the unit ball.
Let B be the open unit ball for a norm on . Let f:B → B be a holomorphic map with f(0) = 0. We consider a condition implying that f is linear on . Moreover, in the case of the Euclidean ball , we show that f is a linear automorphism of under this condition.
This article provided some sufficient or necessary conditions for a class of integral operators to be bounded on mixed norm spaces in the unit ball.
We give a new constructive proof of the composition rule for Taylor's functional calculus for commuting operators on a Banach space.
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 and suppose f vanishes outside of a compact subset of , 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 -sense. Set . Then F(x) = O(log²r) as r → 0 in the -sense, 1 < p < ∞....