Carleson measures for Besov-Sobolev spaces with applications in the unit ball of $C^n$

TL;DR

This paper explores the relationship between Carleson measures and Besov-Sobolev spaces in the unit ball of complex n-space, providing characterizations of operators and multipliers through these measures.

Contribution

It establishes new connections between Carleson measures and Besov-Sobolev spaces, and characterizes operators and multipliers using these measures.

Findings

Characterization of Carleson measures for Besov-Sobolev spaces.

Connections between Carleson measures and p-Carleson measures.

Characterization of Riemann-Stieltjes operators and multipliers.

Abstract

This paper is devoted to give the connections between Carleson measures for Besov-Sobolev spaces $B_p^\sigma (B)$ and $p$-Carleson measure in the unit ball of ${\bf C}^n$. As applications, we characterize the Riemann-Stieltjes operators and multipliers acting on $B_p^\sigma (B)$ spaces by means of Carleson measures for $B_p^\sigma (B)$.