On Distance Estimates and Atomic Decompositions in Spaces of Analytic Functions on Strictly Pseudoconvex Domains

Abstract

Abstract. We prove some sharp extremal distance results for functions in various spaces of analytic functions on bounded strictly pseudoconvex domains with smooth boundary. Also, we obtain atomic decompositions in multifunctional Bloch and weighted Bergman spaces of analytic functions on strictly pseudoconvex domains with smooth boundary, which extend known results in the classical case of a single function.

On some new sharp embedding theorems in minimal and pseudoconvex domains

“…Similar results with similar proofs were obtained by the first author in tubular domains over symmetric cones (unbounded domains) and bounded strictly pseudoconvex (nonsymmetric) domains (see [3], [29], [30] and references there).…”

“…We supply three lemmas from [33] which are crucial for the proofs of theorems relating to the minimal domains (Theorems 3.4 and 3.5). Analogues in tube and pseudoconvex domains can bee seen in [3], [18], [29], [30].…”

“…The theory of analytic spaces on general admissible domains has been welldeveloped by various authors during last decades (see [3], [6], [8], [10], [12], [14], [15], [16], [20], [23], [26], [29], [30] and various references there). In this partially expository paper we will turn to the study of certain new embedding theorems for some new mixed norm analytic classes in strictly pseudoconvex domains in C n with smooth boundary.…”

On some extremal problems in Bergman spaces in weakly pseudoconvex domains

“…This paper deals with certain new applications of recent deep results on Bergman projection with positive Bergman kernel in Bergman type spaces in general Ω domains like smoothly bounded pseudoconvex domains of finite type m in C n with Levi form which has at least n−2 positive eigenvalues at each point of the boundary ∂Ω and related domains to extremal problems related with distance function. This paper can be also considered as direct continuation of our previous recent papers on this topic (see [2], [14], [15], [16], [17]).…”

On an estimate of a distance function of several variables and related problems

“…Proof. The proof follows standard scheme we provided in [3], [2], [15], [21]. And the new ingredient is application of Minkowski and Youngs inequality which leads to generalizations of our previous results (case δ = 1).…”