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On some inequalities in holomorphic function theory in polydisk related to diagonal mapping

Romi F. ShamoyanOlivera R. Mihić — 2010

Czechoslovak Mathematical Journal

We present a description of the diagonal of several spaces in the polydisk. We also generalize some previously known contentions and obtain some new assertions on the diagonal map using maximal functions and vector valued embedding theorems, and integral representations based on finite Blaschke products. All our results were previously known in the unit disk.

On some new sharp embedding theorems in minimal and pseudoconvex domains

Romi F. ShamoyanOlivera R. Mihić — 2016

Czechoslovak Mathematical Journal

We present new sharp embedding theorems for mixed-norm analytic spaces in pseudoconvex domains with smooth boundary. New related sharp results in minimal bounded homogeneous domains in higher dimension are also provided. Last domains we consider are domains which are direct generalizations of the well-studied so-called bounded symmetric domains in n . Our results were known before only in the very particular case of domains of such type in the unit ball. As in the unit ball case, all our proofs are...

On some extremal problems in Bergman spaces in weakly pseudoconvex domains

Romi F. ShamoyanOlivera R. Mihić — 2018

Communications in Mathematics

We consider and solve extremal problems in various bounded weakly pseudoconvex domains in n based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces A α p in such type domains. We provide some new sharp theorems for distance function in Bergman spaces in bounded weakly pseudoconvex domains with natural additional condition on Bergman representation formula.

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