External Area Integral Inequality for the Cauchy-Leray-Fantappiè Integral

Abstract

In this paper we extend Luzin inequality for functions defined by the Cauchy-Leray-Fantappiè integral on the complement of a convex domain in C n .

Constructive description of analytic Besov spaces in strictly pseudoconvex domains

“…To prove this we apply T 1-theorem for transformations with operator-valued kernels formulated by Hytönen and Weis in [10], taking in account that in our case concerned spaces are Hilbert. The proof of this theorem goes along the lines with the proof of the area-integral inequality for Cauchy-Leray-Fantappiè integral for strictly convex domain and complex ellipsoids from [18,20]. However, the consideration of outer normal as a region of approach allows us to consider strictly pseudoconvex domain optimal in sense of smoothness.…”

“…In 1984 E. M. Dynkin gave a constructive characterization of holomorphic Besov spaces in simply connected domains in C with "good" boundary. We continue the research (see [17,18,19,20,21,22]) devoted to the constructive description of spaces of functions of several complex variables. In this paper we consider Hardy-Sobolev spaces in strictly pseudoconvex domains with C 2 -smooth defining function.…”