We characterize Carleson measures for the analytic Besov spaces. The problem is first reduced to a discrete question involving measures on trees which is then solved. Applications are given to multipliers for the Besov spaces and to the determination of interpolating sequences. The discrete theorem is also applied to analysis of function space on trees.

For 0 ≤ σ < 1/2 we characterize Carleson measures µ for the analytic Besov-Sobolev spaces B σ 2 on the unit ball Bn in C n by the discrete tree condition

No abstract

We introduce a notion which is equivalent in the Heisenberg group H to that of segment normal to a surface. Then, we study some regularity properties of the function measuring the Carnot-Carathéodory distance from an Euclidean surface S in H in terms of the regularity of S.

No abstract